Registry of deeds doesn't have to be a function of government. Since in modern times a government is always around, it becomes a convenient registrar, but it doesn't have to be this way. In order to defend a title to the property any unambiguous and credible evidence would do; it could be documentation kept by a private party or simply fences, monuments and other artifacts traceable to the owner present on the property itself.
In any event, the need for a registry doesn't translate into a need for a national in scope government setting restriction on foreign ownership.
There is no land ownership. It is an illusion. It's pretend. It's not something you can find in nature.
Thus, if you're going to play a pretend game, you need a government so that you're "rights" to that land can be protected.
The fact that real property is not something found in nature, means that it really isn't a right. It is something that can only be born from an agreement that is made between all of the inhabitants of a territory. It is an invention of the mind.