Frankly, I am not too sure about those insurance companies, but I am sure some do pay off. I had a somewhat similar experience but in a motor vehicle. I was legally stopped at an intersection when two other motorists had a collision which I had absolutely nothing to do with. One of the drivers was slammed out of control and broad sided my vehicle very hard. I ended up going to the hospital with a concussion. I contacted the insurance company of the person charged with causing the wreck. Apparently this was not his first wreck. His insurance company used a simple expedient for not paying the damages. They simply did not pay, and they refused to answer any and all of my phone calls. They also never set an appointment for looking at the damage. They just ignored it all.
The only time I got an answer from them was after contacting the state insurance commission, and then it was a lowball offer with not one penny for medical bills, and a requirement that I sign a statement that my insurance claim was bogus. Talk about crookery.
If the culpable party is not insured at all, I don't have any idea how you might get compensation for damages. Insurance companies are in business for profits. If they can get away with not paying off, they will. If there is not any insurance, well, you'd need a lawyer for that advice. I understand there are lawyers who might specialize in motorcycle and bicycle accidents.