On the other hand, we have read reports by those who claimed they had bought shares at the Bid. If you
can give me a sensible reason why this has persistently been reported, then I will be willing to say that a
fair market has been made in this security.
Actually, what you're willing to concede is the answer to your question: In a fair market, you can buy at the bid.
In my experience, it's not even remotely unusual to be able to buy stock at the bid. When I buy, I do so at the bid. When I sell, I do so at the ask. I usually fill. Sometimes I don't. If I'm not having any luck and either really want the stock or want out of it, then I'll sell at the bid or buy at the ask, which is almost always an immediate fill. If you buy at the bid or sell at the ask, you wait for a willing seller or buyer at your price.
For example, if I place an order to buy 1000 shares of a stock at 13 1/4, and I'm the highest bid, I'll get filled when any of the following happens:
1. Someone sells 1000 shares at market
2. Someone sells 1000 shares at a limit of 13 1/4 or lower
Whether you can buy at the bid depends only on whether someone's willing to sell at your price. If you're the high bid, the next sale at your price (or market) will go to you if things are running as they should.
If you're using a program like QCharts (which I use), it's pretty cool to watch Level II (works for OTC but not OTCBB stocks). I'll put in an order and see it show up and can see when I'm the inside bid or ask (usually next in line for a fill).