Tossing another anecdote onto the pile, I just searched "Adidas shoes". The first four hits are not for Adidas shoes, after that they all are.

All four of those non-Adidas hits are "Sponsored" results, but that's not particularly easy to notice (for one of them it's almost impossible).

I would agree with GP that Amazon product search often leaves much to be desired. It's hard to search for X without getting accessories for X, competitors to X, products that can be connected to X. This is annoying at best, and crippling if you want to, say, sort by price (all the cheapest matches will be accessories or otherwise not what you wanted).