A couple of months ago I read a couple of threads on 2p2 about Bayes theorem and it's application in something that sounds similar to this and the conclusions people came up with were oddly dissimilar. Since you're clever enough to actually figure out the maths and it'd be a bit of a struggle for me I'll just throw out some of the ideas I remember from it.

If you sit down with a player you have never seen before and he doesn't put any money in once in ten hands you already have a strong indication that he's unlikely to be a 30+ vp$p player. Similarly, if he hasn't raised with PFR. Similarly, if he plays 8 out of the first 10 hands he's unlikely to have vp$p under 20%.

We can never achieve 95% confidence in any stats as no player plays completely mechanically - most are not good enough to do that, and those who are will be good enough to adjust. All we need is a ballpark figure. High or low is enough to get us started in terms of extracting value from stats.

It's very true that 20 hands doesn't tell you for sure if someone is 14/11 or 16/12 but it can point you in the right direction. Whatever information you have to work with is the information you have to work with - and while it's good to assess its quality you're often better off working on slightly inaccurate assumptions than completely disregarding what little you do know.

I guess what I'm saying is - what we'd want to judge based on our stats is not if they are completely accurate but rather how likely they are to be completely and utterly wrongheaded and misleading.

This said I COMPLETELY agree that reads are better than stats. Any hand shown down by any player is a valuable source of information as it will tell you exactly the decisions this player made with this pocket holding every street along the way. Treasure trove.