The 125% number actually comes from sizing the ampacity of the branch circuit for a branch circuit that is considered "continuous" (by NEC definition this means will normally be energized for 3 or more hours). You won't oversize any branch circuit overcurrent protection device (fuse or circuit breaker) if you use this rule.
At first glance, one might think that a motor would typically qualify. However, motor circuits usually have two separate protective components. One is the overcurrent protection, the other is the short circuit protection. In a motor circuit, the overcurrent protection is supplied by the overload relays that are part of the motor starter. The fuse (or circuit breaker sometimes) only provides the short circuit protection.
Motor overcurrent protection is sized according to article 430, part III. In most cases we will be using 1.15 service factor motors, so according to 430.32(A), the overload relay setting would normally be 125% of the FLA marked on the motor nameplate. 430.32(C) allows the overload relay to be set as high as 140% if 125% "is not sufficient to start the motor or to carry the load".
Article 430, part IV covers short circuit and ground fault protection. Table 430.52 indicates that when using a time delay fuse (which we are using) for short circuit protection, you would normally size the fuse at a maximum of 175% of FLA. Exception number 1 in 430.52(C) permits you to use the next highest "standard" size rating of the circuit breaker or fuse (the "standard" sizes are listed in 240.6). Exception number 2 allows you to go to 225% of FLA "Where the rating specified in Table 430.52, as modified by Exception No. 1, is not suffıcient for the starting current of the motor". Note that when using class CC fuses, the code is even more generous.
