As much as I hate Trump and find him to be an embarassment of the highest magnitude, I don’t buy this one either. My WAG is that some German official, speaking on background to a reporter, said something like, “So, Merkel comes over here and this guy not only refuses to shake her hand he literally* gives her an invoice for the $300 billion he thinks we haven’t paid NATO, because he’s too stupid to understand that’s not how NATO works!” And that somehow evolved into this story. Not that I think Trump wouldn’t do it, just that the evidence for it is ridiculously thin, and, as JohnT notes, if Trump had done that, he would have bragged about it.
*literally: adj. figuratively