Yes and no.
UTSW/Baylor- hell yes. Big research schools. Not to say you can't get in without any but some people have akin'd it to playing behind the eight ball
TAMU,TTU's,UTMB,TCOM-Not really so.
That said having research has made interviewing easy so far. When you get a Ph.D interviewer it helps break the ice and provide some nice discussion.
That said in regards to the UTSW "auto-invites"
my guess is the criteria for the first round was 3.8+ and 35+. If you check the MDapps of those who gotten the first wave of invites, this seems to be the average numbers