What's your source for the claim that Tesla's system "doesn't detect stationary objects"? From the reference frame of a moving Tesla, both globally stationary and globally moving objects will appear to be in motion.
Teslas on autopilot have collided with many stationary objects that were partially blocking a lane. Known incidents include a street sweeper at the left edge of a highway (China, fatal, video available), a construction barrier in the US (video), a fire truck in the SF bay area (press coverage), a stalled car in Germany (video), a crossing semitrailer (NTSB investigation), and last month, a fire company truck in Utah.
Yes, but the radar has poor angular resolution (but a good idea of relative velocity), so it cannot tell the difference between a stationary object at the side of the road and one in the middle of it, so it must ignore all stationary object (by ignoring all objects with an apparent velocity approximately equal to the speed of the vehicle) in order to avoid constant false positives.
It's good at determining whether something is moving towards it or away from it, but bad at determining where that object is; whether it's directly in front or slightly to the left or far to the left. Its "vision" in that sense is blurry.
Poor angular resolution means you can't tell if an object is at 12 o'clock vs 1 o'clock. It means you can tell there are things, but you don't accurately know what angle they're at.
The NTSB report said that the system didn't apply the automatic emergency braking. That either means it didn't detect the stationary object or did it on purpose.
You can argue something between those two options, but ultimately it is just a semantic argument (e.g. "it just chose to ignore it" which is effectively the same as a non-detection, since the response is identical).