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.
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.