Stealth plane are not completely invisible on radar to begin with, most of the stealth tech are to reduce the radar optimal detection range on the aircraft.
The closer the distance btw stealth aircraft and radar the higher the chances it will be detected.
Even during ops desert storm having f117 going into mission required pain staking effort estimating radar coverage and finding best routes for minimal radar exposures.

The true stealth technology like plasma stealth and active radar cancellation technology are still not fully developed yet.

Yup currently all known plane is no radar proof.
Yes stealth technology is to reduce rcs by the means of using shape designed, radar absorbance material, reduce heat signature and reduce electronic emissions.
Rather than giving back wrong info, it rather avoid and divert radar wave away but it still can be detect if get close enough.
Sure you can collect signature of such planes but the problem is you can only detect it if was close enough to your radar. But with signit and proper mission planning the aircraft would just slip through your radar system and all sort of early warning system.
For example a visby class stealth ship it have been said radar can only detect it within a range of 50km.