It seems to me that if enough people say they are something, at risk if suicide or murder, they are believed without any statistical evidence.
And in this case, as the OP notes, this stuff has become part of the belief system. So of course someone claiming to be trans is likely going to claim to feel suicidal. To not do so would be letting the side down, and not being properly part of the group.
And in a survey, where it's not really about them as an individual, of course they'd want to get the numbers up. What incentive would they have to tell the truth? High "suffering" numbers help the cause.
Not sure how much that would have been an issue whenever some of the commonly used/misused stats were done, but I'm sure it would have been a factor, particularly if recruited from online-type spaces, and it will be even more of a factor now.
This is just one of many trans "tropes" like having period symptoms, being unable to open pickle jars, having some intersex characteristics. People aren't prone to making just one persistent counter-factual claim - stopping at sex.
Actual real evidence does exist for some things, and I've never seen a real data source indicate anything terribly out-of-line. Murder rate is normal or low, suicide rate is normal (adjusted for other mental health issues - co-morbidities are notable). GIDS gave numbers and said they had very, very few instances; children in particular almost never commit suicide, even if trans-identifying. Oh, and evidence for transition improving mental health is very poor - this has been confirmed by recent court cases.
Crime commiting rate is somewhat higher - particularly sexual offenses - but that's likely confounded by post-crime transing in prison to claim privileges. Nevertheless, transvestism has long been known to be relatively common among sex offenders, and so the cross-dressing sex offender cohort is now under the trans umbrella, boosting that stat.