Show me reputable proof of either of those two things happening. Keep in mind a female athlete having high testosterone is not adequate proof of anything — some cis women have high T, especially some with an athletic build. And also a trans woman with elevated T is also still a trans woman, so you’d really need a quote in which a person *admits* to faking a trans identity to compete for your claim to be reputable. Identity is identity, so trans women belong in women’s spaces no matter their hormone levels or anatomy.
Again, I would rather allow for the absurd and nonexistent possibility of a trans impostor than risk a trans woman be treated as a man.