That portion is anecdotal. These stories come from either before there were ethics guidelines in psychology so people were studying their own children, or reviews of child abuse cases where the parent was forcing a different identity on their children. This is not something that is possible to (ethically) run an empirical study on, unfortunately.

I was actually repeating what was said in a video I watched yesterday so I went to look at their sources - here is a relevant study that supports this conclusion - https://www.sciencedirect.com/science/article/abs/pii/S1743609515339060

However while looking it up in google scholar I did find another study that concluded the opposite, that there’s no significant difference between identical and fraternal twins. That study is here. https://www.nature.com/articles/s41598-022-17749-0

So it’s possible that I was misinformed.

As a bonus, here’s an interesting analysis about what even is gender and gender identity in an academic setting. https://academic.oup.com/analysis/advance-article/doi/10.1093/analys/anad027/7204699

Gender expression and gender stereotypes are societal constructs. A person’s sense of their own gender is (probably) not. There have been many times where people have tried to raise their child as a different gender than the child was assigned at birth, and the child 99% of the time identifies with the gender assigned at birth, at the same rate as the general cisgender population. There have also been studies of identical twins where if one twin is trans, the other twin often is as well, at a much higher rate than fraternal twins.

There is a genetic component and a constructed component to gender.

Edit: wording.

Edit 2: See my comment below with sources on the twins study - it’s possible I was misinformed on this. The results of studies are mixed.