It the case of Mosconi's run, it was the affidavit that did the trick for the BCA.
With the JS run, they were relying on the video. And that's were those two guy's 14.1 bona fides, or more exactly their lack of, come into play.
Lou Figueroa
Schmidt also had signed witness statements. The BCA must have considered the video to be icing on the cake to the witness statements.
If 'prominent' members of the billiards community like Nick Varner and many others (who have 14.1 bona fides) thought it was a good run, I wouldn't argue with that. The current 14.1 champions also seem to be happy that Schmidt had a great run. (Schmidt already has many runs over 400, so of all the people in the world likely to break Mosconi's run, Schmidt was a likely person to do it.)
After Schmidt's run of public presentation, it doesn't sound like there's any doubt that he ran 626 balls, except for maybe a few fringe players with personal axes to grind.
Schmidt currently has the official BCA record, and that's not disputed.
Some people seem to feel that Schmidt's exhibition run, while longer than Mosconi's, was of a lesser quality because Schmidt made a targeted series of attempts over a number of weeks, rather than just going to a pool hall and doing a run. That's not a big deal for me.