I would think from a legal standpoint, if the state is collecting tax payments on a property, that is considered admission by the state as to who has the legal rights to that property.
In some states, you are correct wrt adverse possession. There are several conditions that have to be satisfied to make an adverse possession claim and one of those is "adverse and hostile"....meaning the person making the claim has to claim that they alone own the property and nobody else does. Some states by law make it impossible to satisfy the hostility requirement unless you pay property tax on the property in question. That usually does not hold for prescriptive easements however. That's not a dispute over ownership of the property - only the right to use said property for some specific purpose.