Technically, this article does not conflict with Bhatia's account on p. 22 of Founders at Work. "It was actually Jack's idea to do that. We ran it by our VCs just to make sure it was OK. When you alter somebody's email, you've got to be very careful."
The article writes, "Tim Draper persuaded the company to include a promotional pitch for its Web-based email with a clickable URL in every outbound message sent by a Hotmail user."
According to Bhatia, Tim did persuade the founders that it was a good idea; it's just that the idea didn't originate with Tim.