This is another reason why having more sensors, i.e. lidar, is an advantage. The more sensors the easier it is to identify things which cause phantom braking.
There is even a term for this used by the people who know what they're talking about: sensor diversity. Elon may be correct that you don't
need lidar, or that "lidar is a crutch", but that misses the point. Sensor diversity, even if not strictly required, makes the system perform better in a variety of circumstances.
I'll go ahead and make a counter-argument against myself though. Every sensing type has false positives. If phantom braking is caused by false positives, then more sensing types means more false positives, and therefore more phantom braking.
Counter-counter-argument: If you use the sensor diversity to seek confirmation of one sensor's detection before trusting it, you can reduce false positives.
Counter-counter-counter argument: If you ignore what one sensor is telling you because another sensor doesn't see anything there, it may be just that the other sensor is having a false negative, and there really is something there, and by ignoring it you're going to get a lawsuit and lots of bad press. (e.g., ignoring radar return from the side of a truck because the camera thinks it looks like sky.)
Counter-counter-counter-counter argument: If you have at least three sensing modalities and sophisticated sensor fusion, it becomes increasingly unlikely to have a false negative on two modalities at the same time. (e.g., Lidar+Radar would see that truck and camera would be outvoted.)
You can keep going back and forth. I leave this as an exercise to the reader.