Have you seen the Secret Service agents trotting alongside the President's vehicle? Or perhaps spotted them scanning the crowd for troublemakers at a Presidential appearance? You can't miss these guys – monochrome suits, sunglasses, always talking into a radio or cellphone as they walk along. Do you think for one minute they're trying to become famous? Of course not. They'd probably dump the suits for jeans and polos if they could, just to look less conspicuous.
Of course, Secret Service agents have been known to blow off a little steam when they're out of the spotlight – say, in a foreign country where they're doing advance work for a Presidential visit. They don't want to become famous there, either, although someone should have thought of that before the party started.