In criminal cases you are presumed innocent until proven guilty.

In civil manners, there is no such protection.

Still, the insurance company should do their due diligence in confirming with their client (you) that the incident did occur before paying out, and by extension charging you.

Is Progressive your insurance carrier?
If not, they have no legal right to demand payment unless you're in a contract with them, admitted guilt, or willingness to settle/pay, have a court judgement, etc.

You did say that they have already sent you to collections, right?
In other words, they're not just stating that they will/can/shall do so.

If all the things check out, this would be a good grounds for extortion and/or tort.