This really, really doesn't follow. [Edit: Kaylin has altered the quoted text to address my concern and added a clarifying following paragraph that improves the overall message considerably, but it is still worth thinking about the unreliability problem explicitly, so I’m leaving the body of the message here unchanged.]

The data analysis here is all very speculative and hopeful, and therefore largely invalid.

Of course, the original ~50% number should be in doubt given the evidence you've presented. But what you haven't done is present any sort of compelling case for any particular number. So we certainly shouldn't consider 50% settled, but that the "male pattern of criminality" hypothesis is debunked by this is completely wrong: practically nothing is debunked by this except any very strong claim that we know exactly what is going on.

The reason why your analysis is fundamentally unable to provide clarity is that it relies upon assumptions that are likely to be wrong and certainly aren't demonstrated.

A fundamental principle of data analysis is that if your data might be skewed by selection effects, and you're trying to draw a contrast across different conditions, at the very least you need the same skew in different conditions (or you need to have a good estimate of what the selection effect is).

In this case, the task is to compare rates of sex offenses of trans people (maybe just trans women, if we're investigating the "male pattern" claim) to those of non-trans people.

You correctly introduce a serious confound: we don't always know who is trans and who isn't.

But you then do calculations that assume that we know every time when a sex offender is trans, but 90% of the time we don't know for any other type of crime. Obviously if they've had sex reassignment surgery we would know in the sex offender case, but given that under 0.1% of people in the U.K. have undergone sex reassignment surgery, either trans people are just fantastically crime-prone in general (boosting their prevalence 10-fold among those convicted of crime), or the 1%/2% numbers contain among them a huge number of people for whom their status as a trans person wouldn't necessarily be revealed during a sex crime.

So you really haven't done anything to get a handle on the differential selection effects of MoJ detection of trans sex offenders who have had a case conference, and the Prison Inspectorate's trans survey. (Note--the survey also doesn't count people with a gender recognition certificate, but since GRCs are rare, it's probably not a major confound.)

To their credit, the info sheet (correctly) says potentially as low as 4%. Well--perhaps it is that low! But also quite possibly not, and thus our confidence is extremely low here. Therefore it is completely unwarranted to conclude that the real figure is "nowhere near the 17% of cis men serving sentences for sexual offenses". All we can conclude that we don't seem to have a good handle on this number, absent better information.

If you want a claim to stay debunked, it helps to have solid alternative information. In this case, that isn't true--the 50% number is highly unreliable, but no reliable number is known. I couldn't find any data from which to do significantly better, either.