The problem here is that the proclamation says otherwise. It doesn't include any exception for current holders

Trump has the legal authority to block anyone from entering for essentially any reason (see Trump v Hawaii)

So it doesn't matter much what the white house says today. They are free to change their minds tomorrow. That's part of the strategy, if immigrants are afraid they will be arbitrarily extorted at the border, then only the ones whose employers have bribed Trump will even bother applying