2009 Honda Fit idle problems?

Your dealer rep is blowing smoke. It’s a lie that a warning light has to come on to prove that there is something wrong with a system. There is something wrong with yours, and it’s a safety concern. Safety concerns get cars recalled pronto.
Call your car maker’s area (regional) representative. Use words like safety, and hazard to get their attention.
I don’t know how your brakes are power assisted…if electric or vacuum. If vacuum power assisted, a vacuum (air) leak in the brake booster, when you press the brake, lets a lot of air go into the engine intake, the engine adds more fuel to match the extra air, and you have a high revving engine which propels the car forward, suddenly.