TCAS systems won't automatically take over. Instead they audibly issue an order to the flight crew, describing the action that must be taken, and the flight crew must take the action.

Instructions from TCAS are near absolute in their priority. If ATC says to do something different, you ignore ATC and do what TCAS says. If the pilot in command says to do something different, you ignore the pilot in command and do what TCAS says. If somehow God Himself is on your plane and tells you to do something different, you ignore Him and do what TCAS says. Compliance with TCAS is non-negotiable, and the Überlingen disaster[1] is the bloody example of why it's that way.

Self-driving/autonomous-car systems need to have a similar absolute authority built in. If Uber disabled theirs because of false positives, it's a sign Uber shouldn't be running those cars on public roads.

[1] https://en.wikipedia.org/wiki/2002_%C3%9Cberlingen_mid-air_c...