Excellent fic. You know, it does make sense that there would some fallout from Clark's declaration that he does Superman's laundry. At the very least, as you pointed out, everyone will know that he is close friends with Superman, so he's going to be a media figure in his own right.
That probably explains why everyone seems to think nothing of it when Clark grabs his tie and says, "I'm going to get Superman" in later episodes.
Although on the show, I disliked Clark's explanation. "Doing laundry" sounds altogether too prosaic for a superhero. Superheroes shouldn't have to worry about laundry, darn it!
(Except apparently they do. I'm reminded of a great bit from one of the "Spiderman" movies, where Peter Parker is washing his clothes in a lonely laundromat late at night, and he sighs to see that the red-and-blue of the Spiderman costume has gotten all over his whites.)