I'm sorry, but this isn't true. As you said, the OLED Model trailer is back, and it was privated for SEO for the Splatoon 3 Special Edition, not due to rights issues. Furthermore, the Nintendo Switch reveal is, like the OLED Model trailer was, privated, and not removed, while mirrors, including those by significant publications, remain up with no licencing issues or georestrictions. If it was licencing related, then the videos would have been removed, not merely privated, they would have been removed from mirrors, or had mirrors copyright struck, and the OLED trailer wouldn't have COME BACK.
Nintendo also employs half decent lawyers, and they have COUNTLESS trailers going back years, dozens of Nintendo Directs, and it's unusual for any of them to go down despite very complicated licencing. In general, trailers such as this have licencing that's more or less in perpetuity, and that's, in advertising, generally the norm. At least where I live.