Watch for yourself. I find the video at the start to be dishonest as fuck. The story bears absolutely no similarity that I can see to the Lion King except that they feature African animals. That's like, literally it. Maybe there's more similarities in the anime (but based on plot synopsis it doesn't seem like it) but I'm not going to watch all that since the movie kinda sucked.
You're correct. This is basically a conspiracy theory more about slamming Disney than investigation. There are a few superficial similarities and sometime in like the 90s the internet ran with it to the point where it's been treated as an unquestioned fact in many corners. Thing was, in the 90s and early 00s the internet didn't really have video blasting from every corner, so the conspiracy could be shown via a few pictures. If the video were widely available the theory falls apart.
Most you can really make an argument for is that Disney lifted a few visuals, but movies do that all the time.