Your'e right. Raising the debt limit is a separate event, in theory there could be a shutdown if no appropriations are passed October 1st, and that was the flavor through 2000.

The idea that there's some sort of forced budgetary event on the calendar, related to the debt limit, that's then raced through to have competing solutions, then laden down with pork is Not Even Wrong, i.e. in the Pauli sense, and plainly wrong.

You raising the October date does leave open that maybe they're thinking of budgets and think the minority party in Congress has peer footing as a solution / is required to make a budget. That, at least, would explain the pork mention.