Case Closed
I spoke with the operator. They referred me to another part of their Terms of Service:
6.2. Fraudulent Activity. If, in our reasonable discretion, we determine that a player has engaged in fraudulent, unlawful, dishonest or improper activity (including, without limitation, the provision of false or deliberately misleading information), we reserve the right to immediately terminate or deny a player access to their Account. In such event, all Account balances (including both deposits and any winnings) shall be forfeited and we reserve the right to disclose information (including the identity of the player) to applicable parties including but not limited to; the Gaming Commission, banks, credit card companies and/or any person or entity that has the legal right to such information, and/or taking legal action against such player.
However, they say they typically don't confiscate deposits anyway even though they can, and they didn't do so in this case, either: Player made a total of $1250 in deposits, and $2500 in withdrawals.
They also say that:
(1) Player didn't advise CS that he would open a second account, he said that he would have "a friend" open an account.
(2) The second account had an address in a different state, but it was really the same player.
(3) The player did an extreme amount of past-posting. (Don't ask for more details, I don't have them.)
They said that if the player is unhappy they can take it up with the gaming commission where the operator is licensed.
I believe the operator. Incidentally, I was skeptical of the player from the beginning because he opened with, "You have been listing Bovada as the top site for online sports wagering...", when actually I do no such thing: I advertise casino only, not sports.
Those of you who doubted the player, you were right. I was skeptical but reserved judgement until I heard both sides of the story. Now that I've heard both sides, I believe the operator. They're more credible.
Thank you very much to everyone who weighed in on this case.