I had a paper log that was really just a running list of dives from back when we used US Navy Tables, but that note book was lost in the drive back to the East Coast from Texas in the days following 9/11.
C-cards and log books just mean that at one time you got your ticket punched, they don't mean that you have ever used that ticket.
Having been on dive boats for over 30 years now, you get good at reading a diver on how they get onto the boat, put their gear away, and rig up. If I see a diver who gets on with little if any fuss, has their gear tight and put away quickly, and sets it all up quickly and correctly, it's a good indication that they know what they are doing.
A bit of wear and tear on the gear can go a long way also, or it can just mean they got it all off Ebay. Its how the whole picture gets put together that matters.
Because of the above, I don't have all that much of a problem with a check out dive, as long as it is short and I am then left alone from all the nanny-ing afterward.
Last, I do recall being in the Bahamas in 95 and having a DM hand me a weight belt with about 15 pounds on it. At the time I was diving in only shorts and a t-Shirt, I asked the DM what I was supposed to do with 15 pounds, anchor the boat? I then asked for a 4# weight to counter the aluminum 80's buoyancy at the end of the dive. The DM replied, "Oh, you'r a real diver," handed me the 4#'s and left me alone for the next few days. Funny thing is, by the 3rd day 3 of the other divers had also shed their weights and were diving like I was after a few 5 to 10 minute talks with them about proper weighting.