No, you're the one peddling misinformation here. It's true that you have to tell German authorities about your foreign business (not just your income from that business) for tax purposes if you're actually operating your business from within Germany (i.e. you're running a "Gewerbe"). There are also some rules to follow you're merely conducting business with German customers, i.e. how to collect VAT etc.

In any case, however, you certainly don't have to "convert" your business into a GmbH.