Using rear backhoe tires with differently worn treads - is it a mistake??

I punctured my tire this weekend on my case580k back tire (17.5 x 24). The tire shop said it couldn't be repaired and that I'd need a new one. They also said that it would not be advisable to run the machine with one new tire and one old tire because the new tire would grip much better and could ruin the differential/gear box. Is this true? Or are they just trying to get me to buy 2 new tires ($599 CAD each!!!!)

Thanks for any advice or insight. I'm in the process of trying to find a used tire but they seem hard to come by....

Ron

Using rear backhoe tires with differently worn treads - is it a mistake??