What's there to test? You have data that says that they start and end on the same frames and you have a guy using a Wavebird controller showing that the moves come out on exactly the same frame.
Keep in mind that you can reverse the Up-B on hit, on shield and on whiff. Doing so with Mario is possible but since the initial hit has little knockback, it's not as safe as Doc's Up-B.
The only thing that's disappointing as far as Doc's power is concerned is how much damage he does compared to Mario (though 14% for a back air that kills early and comes out on frame 6 is pretty awesome).
Mario's moves have low knockback compared to Doc. Combined with Mario's airspeed and jump height, you get better string potential than Doc, but very percent specific combos. Doc gets more consistent combos at various percentages on various characters, but worse string potential due to his lower mobility. As shown in that video and in the frame data, there is no difference in start up or end-lag.
I'll test it anyway if that's okay with you. I'm not sure all that frame data is accurate (where/how do people get that anyway, I've always wondered?). Also, the video was uploaded in December, we've had a few patches since then. I'm guessing my findings will be no different and everything I think is happening is just a placebo, but I'll verify anyway. All I know is I can throw out attacks far quicker as Mario, frame data or not. Again, I'll try and test it to the best of my ability just to know (for my own sake), one way or the other.
If what you're saying is true, I'm surprised more people don't play as Doc. Mario's recovery is very overrated, so that shouldn't be the deciding factor between the two. Hopefully word gets out and we start seeing more Doc's in high level play.
Update: Okay, did some quick testing. The start-ups and cool downs are the same (as expected according to the frame data). But, those things are subject to subtle changes in an
actual match. Here's what I found.... Doc seems to be slowed by something when actually lading a hit. Is it KB? Probably, but I'm not sure exactly. The jabs are the easiest to test. If you do a jab-jab-jab string with both Doc and Mario, they come out and end at exactly the same time. When Doc hits his opponent, however, there is a delay after each hit. Mario really doesn't have that same delay. The same seems to be true with most of Doc's hits. He's slowed/stunned for a bit after a hit.
The thing that was getting me the most I can now confirm is the lag on things like running and landing after a jump. Doc seems to have a slight delay when stopping and trying to start an attack. Mario doesn't seem to have any delay. Again, I'm not sure if there is frame data to back this up or disprove it.
Ultimately, it's the slower speeds that make the difference. With Doc, if I land an attack and try to run up and follow it, I'm often too slow. Same goes for a missed attack (or an attack that was shielded). With Mario, I can land a hit, run up quickly, follow up, rinse and repeat. If I hit their shield, there's seemingly less delay for me to get some jabs or another quick move out.
These are my own personal findings, I may be completely and utterly incorrect. I'd love to have video or data to back it up, but I don't right now. Having played thousands of hours as both Mario and Dr. Mario, I think I can tell the difference, but maybe I'm just a lunatic (people have suggested the latter on more than one occasion). Either way, thanks for the fun and friendly discussion. If anyone has more input, I'd love to hear it!