And to add to Alex's info...

The U.S. credit card needs a U.S. address, but does not need a bank account anywhere. The address does not have to be the same as your M&M address. And, the U.S. credit card can credit miles to the same M&M account number as the German card.

And, Thomas...

The advantages of having two LH VISAs: since I have two currency income streams (€ and $US), I have very few currency exchanges, and at current €/$ rates, I earn 20% more miles on $US transactions. (Also, two signup bonuses was nice.)