Comparing Claude to a personal trainer is not an adequate comparison.
The personal trainer doesn't train for you, he or she teaches you movement patterns and educates you on proper form and maybe also on healthy dietary choices.
It's more like if he was paying for a personal coding tutor, which Claude or ChatGPT can theoretically be as well, but that doesn't seem to be what he did here.
In my opinion, there is an important difference, though: The software that people "create" with Claude, ChatGPT or whatever could have been created by most competent and skilled software developers, i.e. nothing ground breaking or world changing has been created by people using Claude or ChatGPT (at least not as far as I know, please correct me if I am wrong). However, this is different with regards to the iPhone or the light bulb, they were truly historic and world changing "creations".
As far as I am concerned, it doesn't really matter if you were the true "creator" of a certain product, software or invention, as long as you manage to sort of market the product and convince other people of the value of said product or invention (and as long it holds actual value to people).