Log books are worthless for evaluating a student's abilities ... you really need to see them in the water.
I agree whole heartedly.
As the OP noted, anyone can forge a log book, writing down whatever is needed for required dives.
One step up from that is what some people call "tea bagging": getting into the water at a shallow depth, hanging out for a while, going to the surface, going back down, hanging out for a while, going to the surface, going back down.... This gives you a required number of dives, but....
A step above that is doing the same very basic (but legitimate) dive over and over and over and over again. In a thread a few years ago, a woman considered herself a highly experienced diver because she had totaled about 200 dives over 20 years experience. Every one of those dives was done off of a cruise ship in tropical waters, never deeper than 60 feet. I haven't seen her dive, but I would bet I have seen many people with a fraction of that paper experience who have far more real experience and far better skills.
One of them is a student of mine. I was introduced to him when our shop scheduled me to teach his AOW class--scheduled for a few days after his OW class, which he had not done yet. Whoa! I said What's the hurry? Well, we did it anyway. He was fascinated by everything and has since been working his butt off, taking class after class, working intently on his skills. His OW certification was 5 months ago. He has started technical diving training, and he looks very solid with his in-water skills. I would say he is a stronger overall diver than many instructors I have seen.
A key benefit to doing the AOW dive early is that with a good instructor, bad habits can be corrected early enough that they do not get ingrained. A key detriment to waiting too long is that if you really do get a lot of good experience before taking the class, you will not get any benefit from it, and all it will be is a card you might be required to have for certain dives.