Absolutely, and most AEB systems can't or don't do that. Everyone wants a safe AEB that functions correctly in all situations but we're just not there yet.
I think the real question is did Tesla mislead customers into believing their system was more capable than it actually was, thus resulting in them relying on a system when they shouldn't have?
Most AEBs do not brake at high speed because reacting to a false positive can actually cause accidents. This makes sense as the time needed to respond to a situation demands detecting objects at greater range which requires more than just higher resolution sensors because as you get further ahead of the vehicle you have to contextualize what you're seeing.
Tesla's system is attempting to do that contextualization where as most other manufacturers systems are simple feedback loops.
But in the meantime I'd vastly prefer colliding after significant breaking than not.