Here is the current language, which is presented, unlike what I previously remembered, on the Offer Page (before you select a magazine) - this is good, but you do need to scroll down and read the fine print:
Automatic Renewal Authorization: Enjoy the number of issues shown and the credit/debit card you provide will be charged just $2 for each selection. Your selections will then continue annually. Each year, you'll receive a reminder notice specifying price plus processing (and any applicable sales tax) and billing terms for the next term of issues and your account will be charged accordingly. Allow 6-12 weeks for delivery. Your name, address, and account information will be used by MagsforMiles to process and fulfill your selections. Cancel anytime at 1-800-641-3458 for a refund of unserved issues. If a magazine becomes unavailable it may be replaced by another with the same renewal features. For individual use only, not for resale. Please print this page for your records. Enjoy.
This sounds good (except they still do not disclose the renewal price, which is very, very bad form), but I am still reluctant to take a chance of extreme hassle given that apparently the renewal price will be highly inflated and they may make it difficult to get through to them to cancel. If they disclosed the renewal price and made online cancellation possible, then I would go for this.