Did that thread in any way define what it considered "excess amounts" of Prime?
The bottle itself recommends up to 5 times normal dosing in some cases and never mentions lowering oxygen levels or a need to increase agitation... so it's logical to think that up to 5x normal dosage is not considered to lower oxygen levels by the manufacturer...
From personal experience, I dropped a fairly full 16.9 oz bottle into a 75 gal tank once. I have no clue how much ended up in the tank but I'm sure it was a lot more than a "normal dose" (assumably 20+ times a normal dose). I did a large water change (around 50%) afterwards and nothing bad happened...
It is very possible that someone experienced poor water conditions and used a large dose of prime to counter the poor conditions... then saw their fish gapping at the surface due to the poor conditions and the person blamed the gapping on Prime... I read a lot of threads where people are overconfident in their solutions and therefore misplace blame...
But without having read the other thread and probably asking the OP thee a handful of questions the best I/we can do is speculate on their problem/cause/situation...