Personally, I'm on the fence about John Schmidt's 626-ball run.
Do I believe that Schmidt, or any of the "witnesses", are lying about the feat? No, not necessarily.
However, I'm not the type of person that just blindly believes word of mouth. Without seeing something for myself, I simply chalk it up as talk.
Furthermore, the fact that there's 'allegedly' video proof of the amazing run, yet nobody will release it, does raise a little suspicion. I mean, if I did something so impressive, I'd make sure the whole world saw it/knew it!
Bottom line: I don't doubt it could have happened. I'll believe it when I see it. None the less, even if Schmidt's claims are completely true, I still find Willie Mosconi's 526-ball run in 1954 far more impressive - given the old tables; cushions; conditions; traditional high-deflection tip, ferrule, shaft, joint, cue; etc. And, the fact that his historic accomplishment stood unmatched for at least 65 years.