Any company that bills insurance typically charges them more, see windshield replacement, flood damage and the entire US healthcare system. Because of that - it's pretty standard for an insurance company to reject many claims at the outset and see how hard you'll fight it.
You may consider calling this towing company and getting an email quote to move your bike from A - B (record it if they won't), perhaps call around for quotes. Once armed with 'normal rates', simply call them and explain there is no insurance and see if they'll cut the price to that - effectively calling them out on the comment, "what do you care, you're not paying". If not, you do have small claims court and your newly gathered evidence to show you've been gouged at the scene of an accident. Social media posting (facts, not slander) can also create pressure, complaints to the local oversight agency (City Hall, etc) may help. That this happened at the scene of an accident may give you some leverage. Important to note that he didn't quote you the price, only a framework (time and mileage) - so there's some argument there was no verbal contract to pay an amount that would be considered 'unreasonable' by most.
You may even find some human interest angle with a local TV or newspaper ombudsman, using the whole 'preying on the victims' angle.
Just suggestions, of course.
We had a similar problem with an accident here in AZ, same 'what do you care' attitude, cop standing next to me refusing to let a helpful passer-by load the bike on his trailer to take to my home - cop made the tow guy quote a price, knowing their yard was about 40 miles away - he answers "not more than $100". Insurance covered it, so don't know if it ended up $1,000 - but the cop had the note in his book.