>The Stone of Scone getting returned to Scotland is a bad example
The Stone of Scone is a good example of something else, though: if you declare that your king is coronated on a particular stone, when your neighbor conquers you what do you think your neighbor is going to do with the stone? Same thing you would do if you conquered them.
Anyway, James VI of Scotland became King James I of England, which merged the claims, and meant that from then on, claims to the Scottish throne and claims to the English throne would be the same thing.