> how is ownership established if there is no single source of truth?
There is: the county clerk in the county where the land is located.
But at least in some places in the US that's actually just a log of some kinds of transactions (sales and mortgages): you don't have a normalized field in a database somewhere that spits out "this person owns this spot" instead you have to build up from each individual transaction- plus there are transactions that don't take place on the log, e.g. deaths and inheritance or marriage/divorce that could take place outside the purview of the county clerk.
e.g. a married couple buys a house, then one of them dies, and the will is recorded in a different state and leaves their property to their kids rather than the spouse, that sort of update would not be recorded in the county clerk's office in my state.
No, the county clerk records aren’t a “single source of truth”. In the US system, it is possible to convince a court the county records are wrong, and order them overridden-which makes them not the single source of truth.
By contrast, in the Torrens system, whatever the government records say are final. If you are the innocent victim of a mistake by the government (or a fraud against it), the government has to compensate you; but you don’t actually get the land back if it has since been sold to an innocent purchaser.