I have no problem with paying off one's contractual obligation, but this is a different thing from getting summarily cut off (on the basis of some unverified machine-generated email) and then having to wait for days or longer to get it sorted. ISPs are in no hurry to deal with these things fast; they like to "teach people a lesson".
If the ISP is now forced to give up the line more or less immediately, that's good news, but I bet they will still take a few days at a minimum, to teach people a lesson.
Two lines is the best answer for anything half critical.