What size is your spare???? If it's not the same size as the other 4 tires, he is right. Having a different size spare is a no no and should only be done in an emergency. I know on the muscle cars I play with, a different size tire on the drive axle will burn up the clutches in the posi and I'd guess it would be hard on parts and make handling dangerous in you jeep. If its the same size and just worn out, you will be fine with it.
My 03 Rubicon build thread ---> http://www.jeepforum.com/forum/f22/1320quicks-03-rubicon-build-1504699/