Interesting. That means that Twitter's implementation is one that is against the law, as it required me to log in before I could unsubscribe. It also only unsubscribed me from "that type of email", so lo and behold, more spam arrived a few days later.
The clause only applies to certain email. Applicable? "The term “commercial electronic mail message” means any electronic mail message the primary purpose of which is the commercial advertisement or promotion of a commercial product or service". Probably not.
