Square does not support PIN entry for US Debit or EBT Cash/Food cards, this appears to only be a feature in countries where Chip & PIN are mandatory: https://squareup.com/ca/en/townsquare/debit-is-here

Yes, there may be some markets where Square doesn't support PINs. I took your comment to mean that Square doesn't support PINs at all, and that it's because of a physical security requirement. I couldn't resist responding to that, since neither of those has been true for a while.

I'm not going to enter my PIN into someones mobile unless I have a way of verifying the app they are using is really the app it says it is. I can't see how that could possibly work.

Meh. With credit cards it's the banks problem if something goes wrong (and their fault for push a horrible authentication method.)