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It is very far from 'an excuse'.
I think that what snotters is referring to is the media trend that assumes that Generic Brown People kill others because they are innately violent or extremist, and that white people are assumed to kill others because they have transient mental health issues but are otherwise good eggs. Mental health issues could happen to any one of us (so long as you're white, natch!), and killing people can be partially excused by the media using "mental illness" as a proxy for whiteness. That narrative is a privilege that's rarely afforded to non-white killers.
bothwell-
Well, it's difficult to make an ironic joke about that sort of thing without being misunderstood. The issue is toxic, with countless crap 70s TV dramas written by people who had run out of interesting ideas having firmly ingrained the issue in popular expectation (not the only cause, news reporting also has a lot to answer for). When there is something people don't understand, such as random violence, they often try to find easy explanations.
While I'm no statistician, I'm with a school of thought that there is very little evidence that violence by mentally ill people is more prevalent than by people without such diagnoses. It just tends to be documented better (for instance, a lot of domestic violence goes unrecorded) and there is also a very general question about the actual causes of violence even in mentally ill people, e.g. people may have been violent before they became mentally ill. In fact, I believe that quite a lot of mental illness can be interpreted as conditions in which the affected person is actively trying to avoid committing acts of violence against others. But it's a hugely complex topic.
Oliver Schick
There's a risk of stigmatising people with mental illness as prone to violence, which is an inaccurate portrayal. However, if an offence was a direct result of the perpetrator's mental illness, then they get dealt with under Part 4 of the Mental Health Act. This usually involves compulsory treatment in secure psychiatric hospital, followed by very long term community supervision. It is very far from 'an excuse'.