MSTP schools set up the same policies for their MD/PhD and MSTP funded students as far as admissions and other requirements. Students don't know or care how they're funded. The only time this matters is for internationals at admissions time, but the reason is just that some schools take internationals and some don't due to funding reasons. Sometimes the bar for GPA, MCAT, and research experience might be a little higher simply due to the competition involved for limited non-government funding. But, there's not additional requirements such as the GRE being only required for international students as far as I'm aware.
I'm at one of the schools you listed in your earlier post and I'm pretty sure the Bioengineering department does NOT require GRE from their MD/PhD students. I've been hoping my classmate in the Bioengineering department would pop on AIM so I could ask her, but I haven't seen her. Regardless, I don't want to give you false info even though I'm pretty sure, which is why I hope you will e-mail. Please let tge other interested applicants know.