Driver Ran A Red Light And Tboned Me, Should I Give A Recorded Statement To The Driver’s Insurance Company?

This is my first accident. I filed a claim through the other person’s insurance (as instructed by my insurance app Root), and spoke with the adjuster today. My main concern is getting a rental car so I can get to work and handle my other daily business. The adjuster asked for a recorded statement. I said I would feel more comfortable speaking with a professional before doing so, and he got all pushy and rude telling me “since you aren’t being cooperative, this investigation is coming to a complete halt.” I asked if he could at least contact the other driver for a statement as well as witnesses and he told me “No that’s not my process. I need your statement first.”

They refuse to provide a rental car in the interim and after asking my insurance company for advice they weren’t super helpful.

Should I just give in and give a statement in hopes that I can get a rental car faster?

Does this situation warrant an attorney? I suffered a concussion and my girlfriend in the passenger seat whiplash (went to urgent care doctor yesterday).

Other driver’s insurance is progressive, police report filed and I do have contact info of two witnesses. In Denver, Colorado.