For the OP.... It is certainly possible to damage your tractor doing any number of tasks. Back dragging and digging with the FEL are no exceptions.
However, If you use some logic and understand the forces applied, and how they transfer to the structural attachment points, you can alleviate virtually all of that risk. These tractors can do a lot more than many people believe. Obviously things can break, but that goes without saying. I've put many hours on my tractor while moving dirt and doing jobs that it wasn't necessarily meant for, and I have not broken or bent a thing. I don't attribute that to luck.
On the other hand, you can very easily bend or break something when applying forces at an angle, or using speed to move solid objects, or digging with a corner of the bucket, or back dragging with the bucket at full dump position, or not understanding float, or (the list goes on and on.)
Use your head, think ahead, work slowly, and think about how you could damage something before trying it out. Just because something works for me, or anyone else, doesn't mean it will, or won't, work for you.