Burg's comments put Schultz's ability to support pro-Israeli policies at risk; if he's known to be an ardent supporter of Israel for ideological reasons (to the exclusion of concern for Germany), people will be more critical of his motivations when it comes time to e.g. send military aid to Israel.

Calling out your supporters, when being a supporter is politically contested, isn't a good idea. If Burg was lying, he'd be better off saying that Schulz doesn't give a shit about Israel.