I think you're missing "don't" in there. Besides those, Wisconsin, UNC, Wake Forest, and Vanderbilt (secondary comes with interview invite) screen. Mayo technically screens before they give you the secondary, but they make you pay the "processing fee" of $75 before they look at the AMCAS so it doesn't save any money.
It's a good starting point, but you want to double check that with the schools themselves though. It only posts what the school did the prior year and so the information will be wrong if a school changes from one year to the next.
they technically do have a secondary, but i don't think there were any essays (last year anyway). just some forms to get filled out and of course another check to write. i can't remember for sure if they screen or not though, but i was under the impression that they did.