In terms of polls, St John's started the season number 5 and at the end of December was out of the Top 25. That is very hard to do.One of the primary reasons to schedule a real OOC is so that you aren't reliant on other teams. Schedule a real OOC and you don't need to worry about this stuff nearly as much.
The narrative around SJU's OOC was wildly overblown and often misstated in retrospect, but regardless was about SJU itself, not the Big East as a whole. Baylor and Ole Miss not being good probably cost them seeding-wise because those wins were discounted, but the 4 losses to teams that were in the Sweet 16 now, were in the Round of 32 or even on the bubble like Auburn didn't really hurt them that much beyond costing them a 2/3 seed.
Any W over Uconn or SJU by anyone else in the Big East was going to be a "good" win, regardless of location. So every team in the league had a chance to prop up their resumes by winning those games. The problem was wins over basically everyone else were "discounted".
The perception starts with what your roster looks like, which is what effects the various rankings people care about preseason, whether that be the AP, Kenpom, etc. If BE teams have a strong offseason, and schedule real OOCs top-to-bottom, it will help everyone and we won't be reliant on 1 or 2 teams to do the job for everyone else.
In my opinion, it impacted the conference and I agree with you created a false narrative in retrospect. However, the narrative was very real around the time of the PC win at MSG in December.
I was not taking a shot at St John's.
I was simply stating the best team in the conference over the last 2 months did not win a lot of big OOC games and it impacted the perception of the conference. You can disagree of course.