Yes putting bread in the refrigerator does increase the rate at which the bread will turn stale.
So putting the bread in the fridge will decrease the shelf life of the bread so it's not recommended to refrigerate the bread but instead keep it out at room temperature.
The cool temperatures of the fridge allows the bread to recrystallize but putting the bread in the freezer actually makes the bread last longer but not in the above freezing temperatures of a refrigerator.