I have a really hard time believing it. The semi-custom and embedded part of AMD's business is a lot smaller, in terms of revenue, than their CPU and GPU divisions, so putting the future of their GPU business at risk just to put it inside a console doesn't make business sense.
That said, AMD can have developed Navi as every other GPU, but are now working with Sony to make some customization in the architecture to better suit SOny's needs, something they already did with both the PS4 and PS4 Pro designs.
So, in my opinion, Navi designed for PS5 is false, but a custom Navi design to better suit Sony's needs is more than likely... and if MSoft continues its partnership with AMD, they'll have something custom too, whether it's Navi, Vega or something else, we don't know.
Please excuse my bad English.
Currently gaming on a PC with an i5-4670k@stock (for now), 16Gb RAM 1600 MHz and a GTX 1070
Steam / Live / NNID : jonxiquet Add me if you want, but I'm a single player gamer.