If culpability is to be assessed, then let it fall upon the person who was actually at fault, by running a stop sign and entering a bicycle path with a motor vehicle. “No-fault” insurance does not normally apply to bicyclists.
Bad law to begin with, and even worse interpretation in practice.
The bill is from the insurance company trying to recoup what they paid to repair the motorists car. Sending the bill to him is essentially not paying the insurance coverage.