Well, since he won't identify himself, one can't make a case as to whether it is "legally his" one way or the other. However, I think it is reasonable to question the provenance of the tape and whether he has legitimate possession of it since he won't identify himself. Until we can know how the person who possesses the tape came into its possession, we can't say whether or not he possesses it legally. Just "having" something doesn't make it "yours."
As for your second point, IP law is pretty clear. The tape belongs to its creator or to the entity which commissioned its creation, depending on the terms of the original contract, unless one or the other party transferred title to the person who now possesses it. If he had evidence of such a transfer, I suspect he would have come forth in an open fashion.
"Fair Value" assumes a market. There can only be a "market" if one possesses legitimate title to what one is selling. I was not suggesting that $50,000--100,000 is the "value" of the tape (one could argue that the tape is worth seven or eight figures if it came to the open market in a legitimate manner), but rather what I thought reasonable sum for a rightful owner to pay for someone who had cared for their property over a period of time. However, the rightful owner would also be within his or her rights to sue the person who had maintained possession of their property and deprived them of its use and the benefits that would accrue to them therefrom. In other words, by offering $50,000--100,000 to someone who had kept its property in their possession in an, at best, questionable manner, one could argue that the League was being generous.