The House of Representatives has quietly passed an amendment to Rule 22 that allows only the House Majority Leader or his designee to introduce a motion to reopen the government. See link in comments.
It pertains to every situation, but it was just changed at the beginning of October. Coincidence?
Did I misunderstand that it did they change the rule for only this one situation?
So much for democracy..
But it was passed by a vote I assume.