I read it the same way you did, but I'm confused that paying out insurance gives the insurer a stronger claim to property than buying something. Is a wreck at the bottom of the sea only still someone's property if that someone is an insurer?
My very lose understanding is that finding a wreck doesn't confer ownership. It confers salvage rights, and if the owner doesn't compensate for salvage (or the assumed costs of salvage), you get to keep what you salvage in payment.
So when there's no-one who can make a legal claim, and is willing and able to cover your costs - it starts to look a whole lot like "finders keepers". But if there's a clearly defined owner, and they're able to meet your costs, you have no right to keep it.
(For a clearer example - if someone gives your boat a tow, they can't refuse your payment and keep your boat, that'd be absurd. But if you refuse to pay they can recover those costs. Adding a few hundred years in doesn't change this, it only makes proving ownership more complex.)
So as I understand it - when the insurer compensates the owner, they assume ownership of the property. You can't lose something, claim insurance, then find it, and keep both property & payment. So when it comes to salvage - if the insurer can prove ownership and cover costs, it's their property.
Shipwrecks are governed by maritime salvage law, an international set of legal conventions governing the recovery of vessels and properties aboard them.
In a nutshell, the putative owner of the vessel or the properties recovered from it has two years from the end of salvage operations to lay claim to the vessel/goods recovered. If the salvage was not performed under contract, then they must pay fair value for the salvage services, but the sources I found are all over the board on what "fair value" is in that context.
