If stealth avionics involves the minimisation of radar signatures, that is, to reduce the reflection such that the plane appears to be a much smaller object (a bird for example), then why do the enemy not ask what the hell a bird would be doing travelling at 60,000 feet at 600mph ?!
My guess would be that radars automatically filter out object reflecting less than X amount of radar energy in order to reduce on-screen clutter otherwise it would be rather difficult to make out anything on you screen.
Another reason may be that whilst a ground-based radar may pick up a smaller - bird sized object - the radar on a missile may not be powerful enough to pick it up and hence intercept, rendering the on-ground detection moot