It certainly doesn’t mean they can’t request that it be taken down (there are plenty of examples of companies requesting take downs for things they don’t have t

It certainly doesn’t mean they can’t request that it be taken down (there are plenty of examples of companies requesting take downs for things they don’t have the copyright to, or infringed on the copyright themselves, only to turn around and request take down). It also doesn’t prevent deals between Disney and YouTube to prevent public domain works which Disney doesn’t want uploaded from being taken down (e.g. the first sale doctrine allows me to sell DVDs I own, but Amazon restricts DVD selling to only sellers with distribution/wholesaling agreements).