To start with, automotive radar capabilities aren't based on the frequency shift that simple doppler radar uses. It does measure frequency shift, but the main way it gets information is by looking at the delay in features of the "chirp" it emits.
I'm extremely doubtful that the strongest echo on any radar system is related to the relative velocity of the target. Whether the object the beam strikes, either directly on echo, is moving or not has nothing to do with the strength of the return, although it would affect the frequency of the return. The reflective characteristics of the surface and its angle to the beam are the main determinants of the return strength.
If you shine a flashlight at a car, does the reflected light intensity change if the car is moving or not?
I think you're mixing together a few different things here. the part about strongest echoes was describing the way some police radars separate which targets they cared about, and you're right that it isn't directly relevant.
The radar will scan across its field of view and identify all of the things that bounce its signal back over a certain intensity level. Each of those things will get a bearing and possibly elevation from the scan direction, a distance from the time it took the pulse to return, and a velocity from the frequency/phase shift of the returned signal (that's the doppler part.)
So yes, the radar itself certainly sees the stopped car. It also sees the overhead sign next to it, and the soda can beside that. The problem comes in figuring out if any of these matters to driving...
It doesn't know the difference between the soda can (which, with its bottom pointed towards the car produces a much larger radar return than would be typical from it's size,) the overhead sign, and the stopped car.
First generation ACC systems would throw all three of them out as not relevant, because they all show a doppler shift that says they aren't moving (the shift shows they are all moving towards the car at the car's speed.) This would be true even if the car had been moving before, and is why those systems can't be used to a full stop in traffic and cut out at some low speed (8 mph, for example.)
Second generation ACC would remember that the car had moved (if it had been in the field of view and moving before,) and would track it to a stop and remember "that one moved, so it's a car and I'd better not hit it." If the car was stopped the first time it appeared, it'd still be classed as ground clutter and ignored. This is where a lot of the mainstream ACC "full speed/stop and go" systems are even now.
Autopilot/TACC from 7.1 and early 8.0 adds one more layer - it does object recognition against the front camera(s) and anything that looks like a car or truck to the camera's DNN gets coordinated by bearing with its radar returned and treated as a car, even if it was stopped the first time the radar saw it.
The (rare) cases you have now of crashes or near misses are because the camera didn't see the object as a car far enough away (or at all) for whatever combination of environmental or object shape/color factors and the radar hadn't seen it move, so the car dismissed the return as not relevant, like so many other truly irrelevant returns it has to deal with every day.
Autopilot/TACC under 8.1 will go even further. Teslas with 8.0 installed have been making records of their routes, and identifying things that have large stationary radar returns on bearings that appear on or close to the road, and uploading their exact locations to mother Tesla after the car safely passes them. Tesla is assembling from them map tiles of whitelisted objects - the plan is that in the future AP/TACC will stop or at least slow down in response to a large stationary return that wasn't on the whitelist when driving a route that's been mapped, even if the camera's DNN doesn't flag it as a car.
Elon's also talked about temporal smoothing of point clouds from the radar, which would potentially help determine if the returns are objects in the car's path or not and help with the 3d mapping aspects.
(I've never seen anyone say it, but I'm kinda expecting the whitelist to eventually become a secondary map for autonomous driving redundancy - with exact locations of the objects known, knowing your bearing and distance from the object means you know your location.)
