I've never seen a "Times Championship" puzzle before, but if 2:56 is the record, I can envision some exceptional solvers completing a daily Times puzzle in the low 2 minutes.
However, if there are a lot of such ultra-fast times being posted, I suspect solvers typing in pre-solved solutions.
Do the fast posts have time stamps? I suppose one could only be certain of times posted 2-3 minutes after the puzzle was uploaded.