xss is more so the problem in this case
I'm under the impression that he means that text boxes don't filter HTML.. so like, for example, I could register as <h1>trinick</h1> and everywhere my name would display as a h1 element. Unless you're running a copy of Netscape from 1995, your browser probably has anti-XSS protection.
They could use Javascript to steal the admin's cookies and login.
How do you presume they would send the cookies? You're right, they could inject Javascript that would collect cookies, but you're unable to open a connection to an origin other than the current website.