There is no such rule in the NEC. Instead, there is a rule that says that every receptacle that serves a kitchen countertop has to be on a 20 amp "small appliance branch circuit." That rule has an exception that allows a household fridge to be on its own dedicated 15 amp circuit. That is an "it is OK" kind of rule, not a "it must be done this way" kind of rule.
I don't have my copy of the NEC handy. It is possible that the most recent version might have a different requirement. But I would suggest looking for the phrase "small appliance branch circuit," somewhere around article 210.11 (or it might be 210.52).
Charles E. Beck, P.E., Seattle
Comments based on 2014 NEC unless otherwise noted.