The university of Bath study was barely scientific. The researcher was his own subject, and it has never been replicated. Yet it is now accepted as the Truth.

A vastly better way to study the issue would be to analyze video footage from roadways where there are both cars and bikes.

I suspect the greatest danger to cyclists is when the driver isn't paying attention at all, or is not controlling their vehicle, in which case I doubt there's a special mental circuit that triggers an unconscious behavioral response when it detects a helmet.