From what I've read, the tank was probably *not* bought by the PO.
Of course, I'll also ask for written proof that my current gas supplier owns the tank; but I assume they would have that so I would simply expect to doublecheck the serial number, just in case the tank had been replaced unbeknownst to me and to the propane company.
In North Carolina, we now know that ownership rights to the above-ground tanks need to be established at the county level, by the propane company filing and renewing a form certifying their ownership.
So, I will also check with my California county today, to see if a similar provision exists for my state.