The Press Secretary isn't the Supreme Court. Her say-so doesn't change the plain text of the order, and you're rolling the dice as to which any given border agent is going to choose to believe.

Not even the first time this week that this admin can't keep each other aligned.

I'd follow the words of the proclamation/EO over what the mouthpiece says.

I was not aware that she had made this statement as well. All previous reporting from this morning seemed to report back to a Business Insider article that cited only an "unamed White House official who has been granted anonymity to speak on the issue". I missed that it was a reference to a tweet from her specifically (as opposed to one of the countless other accounts copy/pasting this everywhere).

Note that Leavitt's words are any more enforceable though.