Radar can absolutely detect a stationary object.
The problem is not, "moving or not moving", it's "is the energy reflected back to the detector," as alluded to by your second qualification.
So something that scatters or absorbs the transmitted energy is hard to measure with radar because the energy doesn't get back to the detector completing the measurement. This is the guiding principle behind stealth.
And, as you mentioned, things with this property naturally occur. For example, trees with low hanging branches and bushes with sparse leaves can be difficult to get an accurate (say within 1 meter) distance measurement from.