Thank you for the additional information. New expert here. I'm a licensed attorney and happy to provide some additional information since the prior attorney opted out of the question. I hope you find it useful.
First, I do agree with what the prior experts said, but there is more. The insurance company has a vested interest in not paying the claim, so if the adjuster can find any reason not to turn over money, it will deny you payment. That said, you do have recourse, both against the owner and the driver, and if you decide to pursue a lawsuit, everyone involved should be named. The court will sort out the liability issue.
As far as proving the owner was lying, there are numerous ways to do that. You could take a look at the traffic report for your accident and see if there are any notations that would indicate a stolen vehicle, such as a hotwired car or anything to that effect. Chances are there are not. It sounds like the driver had a regular key, especially since you said the driver was being followed by the husband and the car contain work tools, etc. A regular key and no evidence of tampering of the vehicle is evidence that there was no theft. You could have the car examine by an expert for signs of tampering consistent with theft. Another thing to do is question (perhaps through that process of litigation discovery) what the circumstances were that led to the alleged theft, and whether they were such that the owner of the vehicle was negligent in supposedly allowing that to happen. For instance, did the owner and leave the shed open and unlocked? What kind of lock was on the shed and could it be visibly seen that it had been tampered with or broken, such that if the car was stolen a report could have been made earlier? Is there a history of auto theft in the area such that the owner should have taken better care with the type of lock on the shed or should have left that shed closed? Did the neighbors notice anything strange that could indicate the possibility of theft, or did they see the owner in or around the shed more recently than the car was allegedly stolen, or perhaps saw the owner even driving the car? Do the neighbors know or have seen the alleged thief, such that as to indicate that the "thief" was a friend or relative of the owner and thus the vehicle was not really stolen? How about an online search that may help uncover the relationship between the parties?
These would indicate owner negligence and/or fraud that would hold the owner responsible or show that the owner is lying. Providing the insurance adjuster with this information may or may not be possible and may or may not help, since were talking about an insurance company here. The information may be obtainable through, as I mentioned, the process of written discovery after a lawsuit is filed, though. Either way, it sounds like you were seriously injured and a lawsuit, as mentioned, should name all parties to protect your interests There is responsibility here, and you are entitled to compensation for your injuries, pain and suffering, etc.
You could do on this yourself, or hire an attorney in your area to handle this for you so you can focus on getting well. If you choose to hire an attorney, a good referral source will be your county bar association. There will be no charge for the referral and no charge for the initial consultation with the attorney to whom you are referred. If that attorney takes your case, there should be no out-of-pocket fees or expenses to pay, either.
I hope this helps. If you need additional information or clarification, just let me know and I'll be happy to continue providing assistance. If I have addressed your issue and/or pointed you in a positive direction, please let me know that as well, and please remember to leave a positive rating when prompted, as that is the only way attorneys on this site are credited for the information we provide.