It's more of a general thing with Lawson and Family Mart... Family Mart has this popular fried chicken meal called famichiki, while Lawson has its own called L-chiki (as well as karaage-kun)... and yet people go into Lawson all the time asking for "famichiki" rather than the actual name of it. So it's a bit of a meme.
I figured that was the underlying reason (same as someone going into McDonalds and asking for a whopper). There's a forum thread on nicopedia about "(Famichiki please)", specifically in parentheses to represent mind-reading.