I picked this game up last week, and the gentleman who taught me how to play was telling me that when the Runner mulligans he sets his initial hand aside and then redraws (sans the initial hand). But I haven't found anything to support that. He suggested I look in the FAQ, and I did but there's still no ruling there.

In the rule book this is said about Mulligans;

"After drawing starting hands, the Corporation may choose to take a MULLIGAN by shuffling his hand back into his deck and then drawing a new starting hand. After the Corporation decides whether to mulligan, the Runner decides whether to mulligan as well."

Can someone help me out? Is this a real rule? Can someone provide me with a citation?

Whoever was teaching was incorrect. If you want to mulligan, shuffle your hand into the deck and draw 5 new cards (9 for Andromeda)