When it was time to cancel I learnt that I was actually on a yearly contract - this was a month later so past the cancellation period. The support advisor claimed that I not only received an email but actually opened it, at which point I knew they sent it to the wrong address or were outright lying as my email client never loads remote resources, making it impossible for them to see that I "opened" it. He also refused an IMO reasonable demand of reviewing the call recording (it was just a month ago so they should still have it) to determine who was in the right.
In the end, I simply blocked further payments. When collections reached out, I explained the story above and they went away immediately. Collections ended up having significantly better user experience than the original company.
Best part of this story
We also spent a bunch of time on the phone with TWC directly, and they had no account in our name or any history of our account.