I wouldn’t quite say it the way they did, but it is mistaken to assume that a trans girl was born “biologically male.”
For one, sex isn’t really binary, either: there are multiple traits that come together to be considered the “sex” of someone. For example, there are XY women who have a condition called “androgen insensitivity syndrome.” While some would label all such people “intersex,” the insensitivity can actually result in stronger feminine appearance. They definitely would have been assigned female at birth.
For another, there are some studies that suggest that the brain of trans people is closer to that of their chosen gender than what they were labeled at birth. And, as @HughGoply says, even our minds are ultimately biological. This suggest then that, e.g. for trans women, at least a part of them was always “biologically female.”
To avoid these ambiguities, the general accepted term is now “assigned male at birth,” or AMAB. And, of course, as I used above, there is also “assigned female at birth” or AFAB.