Auto Insurance Claims: wrecked borrowed vehicle, insurance fraud, insurer

Question
Here is my situation.  My car was broken into and not drivable.  A friend loaned me her car to use until mine was repaired.  I got into an accident (my fault, rear ended a car).  I tried to place claim with my insurance but was told that insurance follows the car not the driver.  Let me state that my friend HAD given me permission to use the car.  When she found out she had to claim it on her insurance, she told her agent that I had taken the car without her permission.  She then explained to me that then her insurance would repair the cars and then file with my insurance to recover the damages and it would not affect her rates.  She is telling me to lie to her agent and say that I took the car without her permission.  It is my word against hers.  If I had taken it without permission and then her insurance filed with mine, would mine pay the claim or try to sue/prosecute me?  I feel guilty about the accident but am afraid to say I took the car without permission when i did not.  Any advice appreciated, thanks!

Answer
Do not follow her advice.  She is wrong on several levels.

First, this is insurance fraud, which is a felony.

Second, there is no free ride.  If her insurer believes you took the car without permission, they will pursue your directly to pay for all damage from the accident.  Your insurer will not pay if they believe  you did not have permission, as all policies exclude coverage for non-permissive users.  Her insurer will then sue you directly.

Third, she is accusing you of a crime, (veh theft or unauth use of veh) which is a felony in most states.

You should tell the truth, and explain to her that she should also for the reasons noted here.  She has already lied to her insurer which is a problem.  But if she comes clean now, they will almost certainly handle the claim correctly and not go after her.