That's the thing. They can't come out and claim it. Because nobody can replicate the mod itself perfectly and prove they made it alone. So downloading it isn't any better. Because they can't remake it, they wouldn't be able to make a video showing how they did it. They didn't come out with it before because they failed to recreate it to make a new video.
They literally can't do anything to prove it, so there's no point in doing anything but leaving it alone.
It also would take a massively long time for people to get close to the quality of it, and people gave up months ago. Never mind the video is potato quality so it's extremely difficult to get close to its bad quality picture. So of course nobody came close. It was an awful video to try and compare to. People already proved that the hats with jiggle physics are completely moddable, which was the only decent point to give the leak at the time.
As for it not being taken down, Nintendo only ignores video stuff if it's fake. They've taken down every leak possible, even their own video leaks with a perfect track record. A literal image they don't always take down, but gameplay videos(again, this includes their own they accidentally have up), they make sure it's gone. They're hyper consistent with it. They would not have left it up in any real scenario. They can't. A video leak is a breach of an NDA from an employee who took the video. Now here's the key thing; other companies trust Nintendo to remove any video leaks they find, since it breaks NDA in the first place. This outright means that companies cannot trust them to keep the NDA factor in check. It's meaningless if you don't try to catch leakers or actually bother to enforce the NDA in itself. That's why Nintendo always enforces their NDA's. They've even fired a person who leaked they had a character's voice, which shows how adamant they are to combating leaks. They've also make Byleth next to impossible to find out, made sure barely anyone knew that Ultimate was going to have all veterans(no leaker could even say that, as they only knew a slew of characters. Contrast Smash 4 where the base roster was leaked among two users, and they didn't go as hard on that one outside of the video). They've gotten tougher on leaks since then, especially since Sakurai really really hates leaks and enjoys surprising people. He actually got miffed that people put the cutscenes from the SSE online, and that's one reason he outright remove cutscenes from 4 as an option, neutering Adventure Mode quite a bit. The other was how much time they took, of course, but he wants people to find out by true surprise.