I'd say exaggerating to the extreme rather than faking, but yeah, I find it hard to believe that she really can't tell the difference - I get it when it's hard for her to produce the respective sounds, but that doesn't really explain her indifference to vowel lengths - and we do have those in German. Teehaitches are a different matter, obviously.

Also, it might be the context, but she seems to be able to deal with these words just fine when used in a sentence, so something does seem to get processed there, but I'm guessing she's not aware enough of that to reproduce those sounds she processes, because she might hear and understand them, but something's getting lost in the process.