Interesting, as most people generally only think of a heat pump, central air, or air handler or commercial refrigeration units when applying this rule, but the way it is worded the OP could have a small heater inside his cabinet the only purpose being to prevent condensation and the rule should still apply.
Any equipment with refrigerant compressors generally will need power for servicing if refrigerant ever needs pumped, or to draw vacuum on refrigerant lines for normal servicing, but most other HVAC may never require electric power for common servicing procedures. This statement is just a general statement and has nothing to do with whether the code is right or wrong with its requirement of a receptacle for servicing this equipment.
Something tells me that the cooling equipment in the OP's case would be removed to be serviced(or even just replaced) if it were not working and the receptacle may never be used for such service work.