There are some details you left out, but they're none of our business. I'll presume you were out of the outside travel lane as no one could have hit u minutes later because traffic would have been already backed up behind you. Unless this was like 2am or something.
I'll also presume the other driver got citation(s) related to rear ending you and you didn't get any.
I'm saying this to prompt your action in protecting yourself. You seem to very much be the victim here. Don't let the other guy and his insurance and or lawyer turn that around on you.
This is the time to go on the offensive while everything is fresh.
I've seen and as well personally been screwed by insurance companies. Protect yourself. It's unfortunate that something like this isn't cut and dry but if you have a sizable claim, someone will be trying to cheat you out of it and insurance companies are as crooked as they come!
On another note to everyone....if ever faced with a collision that is clearly no fault of your own, DO NOT give out your insurance info at the scene and let it become record on the police report. Even if you get a no proof ticket, you can easily get that dropped, but you do not want your info out there for the other party's insurance to be able to deal with.
Long story, but you can easily be negotiated to partially at fault between the insurance companies even if you were stopped at a red light with your foot on the brake and got rear ended in broad daylight.