While he was doing that I told him to make sure he just cancelled the newspaper, not my separate subscription to the crossword puzzle.
I told him I realized I was getting a 50% discount on the puzzle because of my newspaper subscription and understood I'd lose that.
He informed me that no, I would not lose the discount. The deal is a discount when you purchase a puzzle subscription if you also have a newspaper subscription. As long as my auto-renew on the puzzle subscription keeps working, it keeps renewing at that rate. And indeed it has kept doing so.
Bonus: I also cancelled DirecTV several years ago, with no problem, when they had a reputation of being very hard to cancel.
I called, said I needed to cancel, and they asked why. I explained that I loved their service, but my Sprint DSL really sucked. Comcast had just expanded to my neighborhood and so I was dropping Sprint DSL for Comcast internet. I can get a much better deal with Comcast if I get a bundle, so I was going for the Comcast Triple Play (internet, phone, TV). Hence, no more need for DirecTV (but if a decent non-Comcast internet service came to my neighborhood I'd probably switch to that and come back to DirecTV).
They cancelled me then with no hassle.