The quote heading this post comes from the findings reported by Eilidh Cage and colleagues  (open-access) who sought to examine how "experiences and perceptions of autism acceptance could impact on the mental health of autistic adults."
Using an on-line survey "to test the relationship between perceived autism acceptance and mental health (specifically, depression, anxiety and stress)" findings are reported based on responses from over 110 people diagnosed as on the autism spectrum. I say 'diagnosed as on the autism spectrum' but as with any internet survey, there is always a degree of 'trust' that autism diagnoses are being reported faithfully just as it is with other labels that were under study: "a high proportion of participants reported additional diagnoses." Indeed, I also note that "11 participants reported that they did not currently have a formal diagnosis of autism" and were still included in some of the analyses...
No mind, the authors sought to 'quantify' autism acceptance given no measure currently exists by asking various questions including "whether they felt that society (specified as the general public, made up of people who did not personally know them) generally accepted them, with “yes”, “no”, “sometimes” and “prefer not to say” as response options." Responses were also sought to statements such as "over the past week, I have felt accepted by society as an autistic person/person with autism" and onward "perceptions of autism acceptance from different sources." This was complemented by responses to the Depression, Anxiety and Stress Scale (DASS-21).
Results: "depression was predicted by autism acceptance from external sources (society, family and friends) and personal acceptance" but anxiety was not seemingly *linked* to autism acceptance. Drilling down further into their results, researchers observed that "greater personal autism acceptance predicted lower depressive symptoms" indicating that variables such as self-esteem might mediate any risk of presenting with depressive signs and symptoms  (see here for my take). This is something that perhaps tallies with other research talking about autistic traits and wellbeing .
The author has also written a piece for The Conversation on her research study (see here).
I'm not quite sure why the ever-fluffy psychological concept of 'Theory of Mind' (ToM) needed to be introduced into the Cage paper given that no measure of ToM was actually included in the study. A quick search of other published research from these authors reveals that ToM is a feature there too . The authors talk about how "Theory of Mind ability may impact on perceptions of autism acceptance" but I'm not so sure that this is particularly important. It's kinda like suggesting that society is completely autism aware and accepting/accommodating but those on the spectrum 'don't seem to understand it' as a result of any ToM issues, which is of course, a nonsense. ToM also still requires a bit more investigation into what it actually means and covers (see here) including the idea that issues with ToM might themselves be 'impaired' as a result of something like depression (see here). I'd also point out that quite a few other over-represented diagnoses potentially appearing alongside autism also seem to present with ToM issues  too...
"There is still a long way to go in understanding and tackling the high prevalence of mental health difficulties in autism, but we believe that the social model approach is a useful and positive lens through which mental health outcomes could be improved." That was the conclusion reached by authors on the basis of their findings. I would agree that there is still a long way to go on the topic of mental health and autism and the social model approach - "disability is caused by the way society is organised, rather than by a person’s impairment or difference" - is an option for further research of this kind. But I would also caution that one needs to balance such a perspective with others too (see here), and accept that the organisation of society is not always the most disabling aspect of a person's disability, particularly when it comes to something like depressive symptoms. Indeed, to say that depressive symptoms accompanying autism might merely be a facet of a 'lack of acceptance' or a lack of understanding from society or the individual themselves, risks plunging autism back into some pretty dark times (see here) and is likely to conflict with various other views. From a clinical point of view, it ignores some very serious research on the wide spectrum that is depression potentially present for all-manner of different reasons, being relevant to the equally wide spectrum that is autism (see here for a discussion on how depression might actually be something rather more fundamental to some autism over just being 'comorbidity'). At worst, it may even delay or put people off from seeking timely recognised treatments when depression becomes 'clinical', which could be a rather dangerous path to start down (see here).
Having said all that, I don't however think too many people would argue with the idea that personal perception(s) whether positive or negative are likely to impact on a person's mental (and physical?) health and wellbeing. If one is constantly feeling like an 'outsider' or excluded or feels that ones needs are not being met, added to a possible history of being bullied or loneliness or indeed, with other clinical labels also potentially being present for example, one is likely to build up a mindset appropriate to such a situation which probably includes some advanced risk for depressive signs and symptoms. From that point of view, much more needs to be done to look at the ways and means of impacting those personal perceptions; possibly taking into account other relevant research which has some [evidence-based] suggestions on things like societal inclusion and increasing access to it (see here) for those who want this option, alongside other complementary strategies where some [peer-reviewed] evidence is present (see here) and continues to be produced (Google the 'HUNT Cohort Study' to see what I mean). I say all this reiterating that something like chronic loneliness can very much be a major contributor to issues like depression.
I also understand the calls to make society more autism-accepting which I think most people would support as being pertinent across the ENTIRE autism spectrum (see here). I'm however, a little unsure of the real-life plan and details of the plan attempting to achieve this goal; particularly in the current climate when even getting a timely diagnosis seems to be an uphill struggle and when also many on the autism spectrum are seemingly left to fend for themselves post-diagnosis. Society it seems, is getting much more autism aware (for good or bad based on current media portrayals for example) but not necessarily getting more autism accommodating nor necessarily putting important words into actions. Indeed, one could argue that other societal factors like unemployment and financial hardship readily experience by those with autism are probably as, if not more, important to their experiences of something like depression yet little appears to be done to improve such issues for the vast majority...
As for the "experiences of “camouflaging” [that] could relate to higher rates of depression" also mentioned in the Cage article, I have quite a lot of time for this area of autism research (see here). Particularly the idea that camouflaging is not necessarily an all-female pursuit in the context of autism (see here) and how truly energy-sapping it can be for many, many people on the spectrum...
 Cage E. et al. Experiences of Autism Acceptance and Mental Health in Autistic Adults. J Autism Dev Disord. 2017. Oct 25.
 McCauley JB. et al. Self-Esteem, Internalizing Symptoms, and Theory of Mind in Youth With Autism Spectrum Disorder. J Clin Child Adolesc Psychol. 2017 Oct 19:1-12.
 Rodgers JD. et al. Brief Report: Personality Mediates the Relationship between Autism Quotient and Well-Being: A Conceptual Replication using Self-Report. J Autism Dev Disord. 2017 Sep 16.
 Cage E. et al. Reputation management: evidence for ability but reduced propensity in autism. Autism Res. 2013 Oct;6(5):433-42.
 Wang Y-Y. et al. Theory of mind impairment and its clinical correlates in patients with schizophrenia, major depressive disorder and bipolar disorder. Schizophrenia Res. 2017. Nov 7.