Regarding the accusations, the similarity between Your Name and The Girl Who Leapt Through Time seems like an innocent enough coincidence.
At the video’s 25-second mark, with Your Name still shown on the right, the left half switches to a sequence from the 2006 anime film The Girl Who Leapt through Time, from director Mamoru Hosoda.
It’s a bit harder to brush off the question of why the sequences from Your Name and Nijiiro Hotaru look so much alike.
The video identifies the key animator (the artist who draws the most important frames of animation) for both Your Name sequences as Hiroyuki Okiura, and as Ryo Onishi for Nijiiro Hotaru.