I believe, that the Lien is assessed to the individual not the boat...
How do you put a lien on a person? Seize his birth certificate or passport?
While it is true that the liability falls with the person, the taxing jurisdiction's most effective way to enforce an unpaid liability may be to slap a lien on the taxed property, ensuring that it can never be sold, mortgaged, or otherwise monetized until after the tax is paid. It's possible that they won't care who owns it now, they may just put a lien on it and let the buyer and seller duke it out amongst themselves. Their attitude may be that it's not their problem, they just want their taxes.
I'm not saying that this will happen. But if the seller gets pissed off and walks away without paying, there would seem to be a risk that the buyer will be left with a lien on his boat.
I'm not an expert at this. If an expert were involved in guiding this transaction, this issue would have been anticipated and proactively covered in the contract, with moneys going into escrow until the bill came up, and the escrow agent making sure the payment is made so the buyer doesn't end up with a lien on his boat. But these guys apparently decided to save money by not paying a broker, and this is an example of the kinds of risks you get into when you do that. It's a choice, and even if he ends up having to satisfy the lien by paying someone else's tax bill, he's probably still saving money on the deal. Let's hope this remains a hypothetical worst case scenario.