But the system has the ability to detect whether an object is moving in parallel (i.e. within its own lane) vs. across lanes, right? That would seem to be fundamentally necessary in everyday conditions, e.g. day traffic in which cars are switching/merging lanes.

If the problem is that the system didn't detect the woman moving between lanes, then that seemingly contradicts the police statement that the victim moved quickly enough to surprise the AV and its driver.