Huh, as a native English speaker, I would never say, "We had not called on the servant." I might say, "We had not called on the servant to perform that task" (though that still sounds oddly formal to me). I can't speak to the Danish nuance here, but I don't think called on and called for are actually interchangeable in English (at least not in the American English I speak). To me, "We had not called for the servant" means "We hadn't asked him to come over here," while "called on" only makes sense to me as "asked him to do something in particular." My guess is that you're getting marked wrong for called on because it means something different.
uncalled for... I see what you did there :)
But I think the point stands. There's a pretty complete breakdown of phrasal verbs related to call at this link: http://www.thefreedictionary.com/call+on
Note that call for is defined: To appear, as on someone else's premises, in order to get—"The chauffeur will call for you at seven." That's the sense that I think is being used in the Danish sentence above.
Call on is defined: to order or request to undertake a particular activity—"called on our friends to help." I think the song you're referring to is still referring to that sense. (The speaker is calling on the listener to perform the role of a friend as needed).
I think the speaker in the Danish sentence is just talking about whether the waiter got signaled with a hand gesture or something similar, not whether the waiter was called on to undertake something in particular. (I switched to waiter because I tend to translate tjener that way in my head, which also makes the example clearer to me).
However, as you say, you "think" the song and the sentence "refer" to the senses explained in your definitions. The context is not given in either. Therefore, I think 'on' should be accepted (in my opinion). And, as other English speakers here have stated (and I am an AES) that phrasing is used, though I agree with mdn73 about leaving out the preposition altogether.