L.P.
I actually work in medical claims for a major auto insurance company. Your attorney can subpoena that info from the person who hit you if that person will not authorize his insurnace company to release the info voluntarily. Attorneys subpoena this information all the time. I frequently have to obtain and provide policy information on our insured's policy limits. A declarations page would provide that information, or something like a certificate of coverage. Either would show you that persons policy limits. Those documents can be requested by subpoena. So YES, you absolutely CAN, and SHOULD have that information available to you.
I do agree that your attorney's demand should reflect the severity of your injuries/treatment/income loss, and whatever else you may be entitled to based on the tort option on your policy, but it doesn't hurt to have their limits in the process.
Best wishes to you. If you have any specific questions, please feel free to PM M..