(The usual disclaimers apply here about me not being lawyer nor having a particular understanding of Texas law)
From my understanding of liens in real estate, which should be a similar legal concept, the title is held by the owner of the property (in this case the boat) and the lien is placed by someone who is owned money for "services rendered". When the original (previous) owner sells the boat, he is the one who owes the marina for back fees, regardless of who buys it. The problem is that the title won't be transferred to you by the state until the marina notifies the state that the lien has been satisfied, which will depend on the PO paying the marina whatever they are owed and then the marina will have to notify the state that the lien is satisfied, the state then sends you the title and it's finally your boat. Any fees or debts associated with the boat are not your responsibility, that's between the PO and the marina, so to protect you the state won't issue the title in your name until that all happens.
It's not an unworkable deal to make happen, you will just have to get everybody to talk to each other and probably have to schmooze folks and do some legwork to ensure both the PO and the marina will be happy. (At the marina where I boat my first, they were pretty "cranky" until I got the boat out of there) To protect yourself don't put any money into the boat until you have the title in hand and don't be surprised that you will need to move the boat, so plan on that too. You may need to put some money forward in good faith as a deposit on the boat, hopefully the PO isn't a jerk and makes you take him to court to get it back if the deal doesn't work out.
Balance the hassle of the legwork with the diamond in the ruff you may be getting and make your decision, that's why flippers always low-ball you, they can't make money otherwise unless they get the property cheap enough. [Sorry for the business law class. ;-)]
BTW my brother just retired to Georgetown, funny how the internet makes the world a smaller place.