I don't recall the distance but back in '69 I was told that one of the requirements to become a NAUI instructor was an underwater swim, however they were allowed to surface twice to take a breath so it must have been longer than 75 feet. I agree with the mindset that if you can doff and don your gear at the bottom of the pool and swim around "blind" (aluminum foil inside the mask) and some of the other long-forgotten exercises that we had to do it gives you confidence and if something does go a little haywire you might be more likely to handle it more calmly. I think it can be summed up as something like "really knowing your sh*t." Personally, looking back, I think it helped me to avoid those kinds of situations.
I began diving solo when my dive buddy got pregnant (ex-wife) and did so until recently when my girlfriend became my new dive buddy. After having to assist (or downright rescue) way too many "buddies" I got to where the only divers that I would willingly buddy-up with are people like Bob DBF, who, as we know, is a solo diver so naturally I ended up diving alone. Of course now I have to keep an eye on my new dive buddy but so far I've only had to do one actual rescue and I'll be very careful to make sure that doesn't happen again.