I hear this all the time, and seen it not that often. How many actual catches does a dog make after the prey makes it through a fence? Less than most! (Im not talking about red ones).The biggest problem we have here is 99% of the fences are 2-3 strand barb on top, any dog can jump a fence, Its when they are tired or carrying prey back it can become risky.
I dont lift my dogs over fences, and they jump them all the time, I just discourage them from jumping when chasing.
Each to their own I wish you A.T.B
PS Zip is looking better today she will be fine.
when there tried and carrying prey