It has nothing to do with the fact that you are American. First of all, they have no idea what English speaking country you are from. You could be from the UK or Australia for all they know because they can't tell those accents apart.
I have heard servers tell people of other nationalities this same thing. Do you know why? Because way too many people think that the service charge is a tip, that you don't have to tip, that servers earn a "living wage" whatever that could be. Are they supposed to do this? No, they aren't and some places are very adamant that their servers NOT say this.
So, what do you think that living wage for a server in Germany could be? Did you know they have to pay half of their health ins. premium out of their monthly wages? Did you know that they have to declare their tips? That in many restaurants that they have to tip out to the kitchen staff?
Obviously if they are living in a small village where rents are cheap they aren't expecting large tips, but in a big city, yeah they really do appreciate it.
It should never be more than 5-10% and if the service was poor it is ok to leave nothing. If they remind you about a tip, I wouldn't leave anything either, but I would also tell the manager so that they are aware of this.
So, to end my rant, it is not expected that you tip a lot, they are not as dependent on tips to make up a large portion of their salary like in the US, but they are appreciative. Oh, and don't leave your tip on the table.
(I have worked as a manager in German restaurants and have many friends in this business)