I think you're both sort-of right.

It's my understanding that upgrades in advance are sorted first by status and then by EQM/PQM to date. Once you get on the upgrade waitlist (via OLCI or kiosk or checking-in in-person), it is sorted by status and by the time you were added to the list.

I believe there are two processes - one that runs on demand and one that runs in some kind of schedule. The former ignores status and will let you leapfrog while the latter goes by the book and sorts by status then by EQM (in advance) and then status and check-in time.

The on-demand process runs during OLCI and at the kiosk, and checks to see if there is "O" availability for your flight. If so, you can confirm into it. Essentially, it ignores any upgrade waitlist and focuses only on the passenger who is checking in.

The scheduled process runs at some interval (Obviously at least every 24 hours, but possibly more often) - it's the process that generates an email to you that you have/have not been upgraded. It sorts by status and by EQM/PQM and handles the upgrade waitlist in the "official" order.

I suppose technically there is a third process (don't know whether it's manual or automatic - my guess is manual) that specifically handles the upgrade waitlist. If F isn't full or doesn't board full, the GA looks through the upgrade waitlist and processes it.

That's just how I believe it works - I don't work for US IT.