I checked the instructions for one a little while back (client mentioned possibly getting one) and they were clearly written for US installations, and called for earth bonding back to the main earthing point. I think there was a post here a while back too about older models having an earthing point on the pump which more recent models didn't have as they were class 2.
However, if it's attached to an outdoor socket then I don't see how it can be classed as part of the installation, let alone as a 'bathroom special location'.
Was it an outdoor socket on the house, which could reasonably be used for lots of things, or a specific socket installed on a decking some way from the house just for the tub? That might make a difference I guess if the reason for the socket was known in advance.
David Savery had a video a while back on a hot tub installation which was clearly more than 'just' an outdoor socket, but he was installing specifically for a professional spa install, not a DIY job.
Though if the inspector was right and it should treated as a bathroom, other than ensuring everything on 30mA RCD these days, what else would you do? are there any extraneous parts that need bonding on a typical spa?