there are a number of very different tax & licensing questions implicitly bouncing around in this thread -- "ownership" (individual vs corporation/LLC), "sales & use tax", "import duty", and registration entity (foreign gov't, USA, state). there is some complexity, and there are $ at stake. there are also alot of folks out there that will hide behind this complexity with the idea of collecting (not very hard-earned) fees
some opinions based on our experience with 4 boats owned in two different countries, two different states, with titles held by corporation, joint tenants, and in a "trust". everyone's situation is different, so these opinions might not work for you...
if boat is going to be kept in the caribbean
(no plans for usa visits), then foreign title is fine. if boat is to be kept in the usa... or is to be world cruised by a US passport holder, there are advantages to USA documentation. i don't know the latest, but this presumably requires "importing" the boat, and involves paying duty... but duty rates on used sailboats aren't that very high. there is some chance that you could document it now, and not pay duty until it physically is taken into the usa, i just don't know the latest on this.
if a boat is documented, yes indeed the states have access to the registration info. but, from our experience, the state (e.g. colorado) can't charge a resident sales or use tax on a boat (or other asset) that does not enter the state.
there are lots of folks who advocate "corporate" ownership
to avoid paying sales & use tax. many states have worked around this. the corporate ownership
gig requires paying annual fees
to the registering state... and often lawyer fees as well. our experience (with a CA boat purchase and an OR corporation) was that this was a nuissance, and didn't help us in any way with fees & taxes
all this is definitely worth checking out... but watch out for eager "helpers".