Talon-despite the dire warnings already posted, there is a bit more to the process than meets the eye. First, to your original question, the CG has nothing to do with liens other than recording them. That is their only involvement. The only point to the recording is to give any interested party information about the vessel. They do not examine it or make any determinations as to the validity. What is filed with the CG, is a "Claim of Lien", not an actual lien. A lien is a legal finding by a court that you owe money. There is not enough room here for a full discussion of marine liens, but here is some general information. Since your boat is documented, the yard guy can seek a maritime lien or a state law lien, He gets the maritime lien from a Federal court and it is against to boat, not against you. Upon his application and a showing of an amount due, the Federal Court issues an arrest warrant for the boat and US Marshalls chain it to the dock. You get notice and a hearing date at which you can contest the lien. The yard guy will have to post a bond to cover the cost of maintaining the boat during the process. In my Federal District, the standard bond amount is $10,000.
If he seeks a state law lien, that lien is against you personally. Again, he has to go to state court, giving you notice before going to court to give you a chance to show up and contest. The state court will generally set a hearing date at which you can contest the lien. In most states, (LA maybe a bit different due to its Napoleonic Code legal structure), if the lien and judgment are granted by the court, the guy has to take measures to collect from you personally before asking the court to seize and sell assets to satisfy the judgment lien.
As an aside, the situation described by Pilothouse King is distinctly different from your situation. The bank had a collateral interest in the boats it financed for the dealer. In such a case, they can di just what they did, just come and take the collateral.
I suspect that the yard owner has been hit for the sales tax by the State wither through an audit or he reported it as a sale in his monthly sales tax filings, so he is trying to make himself whole by collecting from you.