A thrust rod is part of the suspension on some suspension systems - BMW comes to mind. They have a bush/bearing at each end and if this is cracked or worn some peculiar handling can result. It's usual to replace all of them at one go on the basis that if one is failing the others won't be far behind. If you're not sure about your mechanic, get a second opinion.
Go back and make them show you what a thrust rod is. Better yet, get another mechanic to find out the truth of the car's condition. My car does not have anything called a thrust rod. If you told us what car you have we might be able to look it up. BMW's have them in their suspension and certain models have occasional failures of that part. Go to the public library and look in Chilton's auto repair manual and as you get an understanding of the part, look at them in your car to see how worn, leaking or cracked they look.
What do you mean "both" thrust bearings? Engines have ONE thrust bearing at the drive end. It's part of the rear main bearing. There is no place for or such a thing as a thrust rod bearing. There is no room for a thrust rod bearing because of the crankshaft counter weights.
I'd like to know what they are calling a "thrust rod" for starters...
Just did car inspection yesterday, however they recommended me to replace both thrust rod bushings(Found front thrust rod bushings are leaking/cracked or worn).
