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Maybe the programming of the fridge will keep it from wanting to get colder, but if you put a fridge in a fridge it deffinetly CAN get colder.
The compressor compresses the coolant, thus, same amount of thermal energy on a lower volume = higher temprature. higher temprature cools down to a lower amount of thermal energy on the volume. then when the coolant goes into the fridge it expands and gets the same, lower, amount of thermal energy on a higher volume, thus, the temprature goes down!
Now, if you put the fridge in a fridge, the compressed coolant won't just cool down to room temprature, but to fridge temprature! meaning that theres even less thermal energy in the coolant before it expands making it possible for the inner fridge to get even colder!