Yeah, there can be a keylogger. Some sites, regardless of the extension you type, process everything as a web page. While you typed or clicked on a text document, the web site could redirect it through a more complex page before showing you the text.
Frankly, I've heard some of the crap your friends have said in the past. I'm betting it's just a rumour getting out of control.
If you have a latest browser, spyware and anti-virus, I reckon you've got nothing to worry about.