The article doesn't actually say that, it's just phrased badly. A Pfeilstorch just provided pretty conclusive evidence for migration between Africa and Europe.

But the theory that birds were migrating to somewhere else is likely older. It's even plausible that bird migration was the mainstream theory/assumption, not the hibernation theory.

Indeed, Google Books Ngram Viewer shows that the phrase "migratory birds" was already in use before the 18th century, so before the first known Pfeilstorch in 1822:

https://books.google.com/ngrams/graph?content=migratory+bird...

The current German term for a migratory bird, "Zugvogel", apparently became common around 1750: https://books.google.com/ngrams/graph?content=Zugvogel%2CZug...