Since my instructors are not on ScubaBoard, I'll speak up. :biggrin:
They gladly accepted my unsigned log sheets, making a copy of the last page of my logbook (to keep with my student records). They had no problems with my logs, even though a third or more are solo dives (which are even less "verifiable" than buddy dives). Computer logs give more profile information than non-computer-derived logs, so that poses no problems. (It's not like hand-logged pages are any less copyable. The point is not to catch "cheaters"; the point is to give honest people an idea of when they're probably ready.)
If someone asked for certification type of the buddies on my buddied dives, I'd look at them like they were asking whether I prefer French or South African shoelaces on my ice cream. I have no idea, except for my buddy-family, what certifications any of the others have. As far as certification numbers, that's even worse, considering that I have many recreational NAUI buddies, and NAUI doesn't even *use* numbers on non-leadership certs.
I suppose perhaps my LDS doesn't really need to put much faith in a logbook. The logged dives requirement is really just for the good of the student, as it gives the student a guideline to work with. (If you've got prospective students making dozens of 20-minute dives to get into a class, something's wrong.) The logged dives requirement is there to give a quick rule of thumb for when you are likely experienced enough to be able to grasp what will be taught next; the actual evaluations, on the other hand, are always done in the water.
For example, they once had a student in a Rescue class. He had problems even setting up his equipment, and when they started off with mask clearing and such, he was not capable. He was removed from the Rescue class and got to take the basic NAUI Scuba Diver course instead. His logged dives said he was ready for Rescue, but he turned out to be ready to start at the beginning, regardless of how many logged dives he may have had. (It wouldn't even have mattered if he had them all on full-dive video, complete with iris shots suitable for identification.

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