What really bothered me was they took the payment method itself as an indication that I wanted a different type of subscription. Check? 1 year subscription. Cash? 1 year subscription. Credit card? oh ho! You obviously want to subscribe from now until the end of eternity! And yes, they told me on the phone that my use of a CC was indication that I wanted to autorenew and that there's not a way to pay with CC that doesn't autorenew (at the time I spoke with them in early 2018).
Basically to the NYT: "because of the payment method you used, we are able to keep billing you" = "you must want us to keep billing you!" and that is complete bullshit.
May I ask how you subscribed? I agree it's pretty shady to offer multiple payment methods side-by-side with different terms, but I also haven't seen a lot of online merchants accepting cash/check.
I should have made it more clear that auto-renewing seems like the default specifically for subscriptions made online through the web or an app.
"Your payment method will be automatically charged $4.00 every 4 weeks for the first year ($1.00 per week).
It will then be automatically charged $17.00 every 4 weeks thereafter, starting on (date) ($4.25 per week).
Your subscription will continue until you cancel. You can cancel anytime."
In your case, you may not have checked a box, but I'd be shocked if there wasn't similar language saying that you were opting in to a recurring payment. (It's not as if they're making you read a 5000-word EULA - it's right there front and center on the page in my case.) Not to mention that this is pretty standard practice across subscription-based businesses.
I do think it is good form for subscriptions to give customers advance notice of when their subscriptions will renew, though, and most don't. I would go so far as saying that I wouldn't mind if this was a requirement.