Start by spending some time reading article 430 for electric motors. Then 440 for air conditioners will make more sense. For a motor or a/c compressor the fuse or circuit breaker only provides short circuit and ground fault protection NOT overload protection. Overload protection is provided by another device (thermal protection, impedance protection, or motor "heaters" for example). In the event of a short circuit or ground fault, due to the low impedance (low resistance) of the current path the circuit breaker will see hundreds or perhaps thousands of amps and will open very quickly, so whether it is a 20-amp circuit breaker or a 60-amp circuit breaker will make little difference. Either of these circuit breakers would trip very, very quickly when subject to an amperage draw of several times their rated ampacity. In the case of a motor, using an inverse time circuit breaker, you are allowed to "oversize" the breaker by 250%, see 430.52; so the HVAC manufacturer has actually been very conservative in only allowing a 60-amp breaker for a 27-amp load. 440.22(A) allows you to size the branch circuit short-circuit and ground-fault protection at 175% of the rated load current of the motor. 440.32 allows you to size the conductors at not less than 125% of the rated-load current. 440.22(C) advises you to follow the Manufacturer's Values as they have already done these calculations for you. When wiring a motor or compressor you must forget everything you learned about wiring a lighting circuit, it is a whole 'nuther ballgame.
I hope that helps.