Priority events have text that reads, "Play only as your first click."

Same Old Thing reads, "click, click, trash: Play an event from your heap (paying it's play cost)."

Can I use SOT to play a priority event from my heap, so long as one of the two clicks paid for SOT is my first click?

No.

It's in the latest FAQ I believe.

It is. Page 7, Card 54. http://www.fantasyflightgames.com/edge_minisite_sec.asp?eidm=207&esem=4

Perfectly consistent. You can't play the Priority as your first click because you already spent that click to use Same Old Thing.