Culture is constantly in dialogue with what came before. The very first anime took their inspiration from Disney; one of the biggest '80s mecha shows got its start from a GI Joe spinoff, while another took heavy inspiration from an adaptation of Starship Troopers. And what "anime" is doing in the '90s is very different from what "anime" is doing in the '10s - doubly so if you're going deeper than Miyazaki (who mostly made very Disney-like westernised things - not a bad thing by any means, but not at all representative of the wider landscape).
In the end talking about being "inspired by anime" is as facile as talking about being "inspired by movies" or "inspired by television".
In the end talking about being "inspired by anime" is as facile as talking about being "inspired by movies" or "inspired by television".