It's not true that there is NO human interaction. You download the MPC app, and go through and there is minimal interaction with CBP. Certainly better
than waiting hours in line, being tired and being asked questions by an officer in a booth. Sometimes the officer just stands at the end of the MPC line and scans,
and waves you through.
Depending on your financial resources, this is what I would do.
1) You buy parents round trip to Qatar - remember that you are NOT using the return portion - so you can make it a 1 week trip or whatever.
2) Book them a refundable hotel reservation in Qatar - remember they are going on vacation.
3) Once they are on that plane to Qatar - have them text you when on plane, you buy them the 1 way ticket to JFK. Don't risk any other airport.
4) YOU (I presume you are a US citizen) fly to Qatar to meet them there.
5) YOU return with them to JFK. You download the MPC too. And when you walk through the MPC line, you carefully put their passports inside YOUR US passport.
Good luck.