"If it was advisory, it would have to go to Parliament.
If not, the result would be binding and Parliament would have no say."

Then there's the third possibility, that an incompetent Tory government that had given the public an undertaking that the law of the land did not entitle them to make tried to bulldoze the thing through in the hope that sufficient hubris would overwhelm their cockup. And let's not forget how they must have been keeping their fingers crossed that we'd vote remain so that none of this would come out and they'd all live happily ever after.