This allows you to use the fuses listed by the VFD mfr for protecting the VFD, as per their UL listing and SCCR rating, without having to worry about the effect that might have on sizing based on the motor HP. This was done because UL requirements for listing of VFDs changed in around 2005 to make it a requirement that the VFD protect against short circuits on the MOTOR side, because there is too indirect of a connection to the Line side OCPD. So bottom line, the VFD is now covering the SCPD protection on the load side, you only have to deal with the size fuse they require to protect the VFD itself.
By the way, this does NOT apply to breakers (although I haven't seen the 2014 yet to check if they modified this). That's why you see in MCCs and other factory built systems where even though there is a breaker feeding the drive, there are fuses too. that gets ignored in the field all the time, but technically, the fuses need to be there, or the breaker needs to be sized to the motor, which might not work for the VFD SCCR requirements. It's a bit of a dance sometimes. That gets even more complex if there is a bypass system for the VFD, I'll warn you, but it's not impossible to keep everyone happy, as long as they truly understand all of the rules and follow them.
Bottom line, if you had fuses and they were sized per the VFD requirements, your city inspector was wrong, he didn't read the entire section.