The present question (moot, because the Senate has not voted in favor of Webb's bill) is whether the President can justify a veto on the spurious grounds that, as CIC, the President has exclusive warmaking power.
It would be an interesting case to present to the SC, but they will never get it.
if he says “correctly....on constitutional grounds” then he limits the playing field. If he wants to talk about justifying on any other grounds, then he needds to say so. IMHO, the question is not as clever as he apparently thinks it is. I suppose the Prez couldn’t veto his own impeachment, but it requires a veto-proof majority to vote for it anyway doesn’t it, even if it were a bill?