I agree with that statement to some degree, but I do believe that the 'right' equipment for the player can make a significant difference (especially if that equipment is properly fit). So many players purchase the wrong or improperly fitted equipment for them and thus never show much improvement. It's the old "Indian or the Arrow..." debate. I believe it's important to test equipment with an open mind (not going in believing you have to have a stiff shaft or brand XYZ), then when purchasing get properly fit (perferrably a dynamic fitting). If a player does this, I do believe improvement is possible (if player is dedicated to improvement).
Of course there is also an issue where new equipment takes some time to get accustomed to and this often frustrates players, who then just go looking for something new. According to my Dad, a PGA Pro, the magic 'elixir' for improvement is positions (aka proper mechanics - usually via lessons), practice, patience and programming (term my Dad used for the mental side of game and course management - he liked keeping them all 'P'). If these elements exist, then proper equipment can make a difference.
(Just as a note, my Dad would also sometimes throw into his 'P' lesson the other elements he thought were important - passion to improve and positivity to believe you can).