Cable company is incompetent. Some people who use cable companies are idiots. Like all services that request an email address, they should verify the email address before using it.
By the sound of it, this is a simple case of the above. Idiot doesn't know their correct email address, Incompetent doesn't verify when given it. OP keeps fixing the situation, only for the idiotic, incompetent process to be repeated.
I get emails all the time from companies because they don't do this. Various idiots with the same, or similar, name to me sign up for something, get their email address wrong, and I end up getting either spammed with junk or fed information about their account. This wouldn't happen if the email address was sent a confirmation email before it's used.