I've thought for years that this was probably the case. It's infuriating. The change of language, as others have said, has not just been a careless or inept choice of words. It's quite obvious that the words transwoman and transman were coined precisely to try to change the way people think about this issue.
Most English words that end in -woman are old-fashioned or obsolete now, but if you think back a few decades, we had policewoman, washerwoman, Frenchwoman and so on. All words designed to make it plain that the person referred to was not just a police officer or launderer or French or whatever the first part of the word was but also female. We've stopped using a lot of these words because in many cases there was no good reason to point out the sex of the individual and it was reinforcing sexual discrimination and stereotyping.
So transwoman was from the start intended to plant the idea that transwomen are women or female. There was a brief period when the people using the word and pushing for everyone else to use it too would say that there were men and women and then additionally there were transmen and transwomen - so straight away they were introducing the idea that trans people are not to be included in their natal sex class.
And once they had that toehold, very quickly the line changed and activists were saying 'transwomen are women, transmen are men. There are two types of women, cis and trans. Trans is an adjective - trans women are women, just like Black women are women.'
And so on. So now we're supposed to accept that trans people belong in a sex class by virtue not of their biology but of their gender identity (which nobody can define or verify).