"Paid for your time" does not mean "work for hire" in the U.S. If someone is not an employee, then only certain types of works can be works for hire: "a work specially ordered or commissioned for use as a contribution to a collective work, as a part of a motion picture or other audiovisual work, as a translation, as a supplementary work, as a compilation, as an instructional text, as a test, as answer material for a test, or as an atlas, if the parties expressly agree in a written instrument signed by them that the work shall be considered a work made for hire." Notably, even a written contract saying "work for hire" doesn't make something a work for hire if it doesn't comply with the statute. That's why it's important to have a proper contract, typically one that says work for hire *and* grants the customer an exclusive lifetime license.
I have no idea of the merits of this case or about German law on the subject, but if the contract did expressly grant a limited license, it's likely that it wasn't contemplated as a work for hire.
I have a theory that it's impossible to prove anything, but I can't prove it.