Margareth Meyer (Zimmermann) - Parents of Margareth Zimmerman?

At the moment we have, as parents of Margareth Zimmerman, Margaret Dunbar Zimmerman and Heinrich Jørgen Zimmerman

Do we have evidence that these people actually existed?

Here are the — they have middle names, in 1480, and both of these middle names are Scottish, not Swiss.

When I go to look for them, I’m finding them in web trees only. Ancestry web tree has them born in England. In which case Zimmerman is a very unlikely name, in 1480, and they would be unlikely to have a child born in Switzerland.