Rear-ended at a red light but other driver's insurer says I'm 40% at fault. Is this even legal?

I was completely stopped at a red light on a Thursday afternoon. The guy behind me was looking at his phone and hit me going probably 30 mph. My car has $8,400 in damage, I have a neck strain my doctor confirmed, and I missed a week of work. His insurance company called me this week and told me their assessment is that I'm 40% comparatively at fault. Their reason: apparently my brake lights had a bulb out that they say contributed to the accident. I never even knew one of them was out.

I'm in a comparative negligence state so they're offering me 60% of my damages which works out to about $5,040. I feel like this is completely made up. I was stopped at a red light. Does a brake light really matter when you're already stopped at a red and there's a lit traffic signal clearly visible? And how did they even know about my brake light - I certainly never admitted it, I had no idea. My guess is they checked my car's photos from when it was towed.

I don't have collision coverage on my own policy so I can't just go through mine and subrogate. Is 40% contributory fault for a brake light thing a real legal position or are they just making this up to reduce my payout? Should I get a lawyer?