Fact: They are required to say that because of some legal nonsense involving a lot more than I am able to elaborate on because I don't know the intricacies of it all.
Also Fact: Any documentary/mockumenatry that states such is only going as far as stating that any recreations of scenes had actor portrayals, and those actors were not harmed. Also applies to filming/production staff, not necessarily any people not involved directly in production.
And an example of the latter would be pretty much every single episode of "A Thousand Ways To Die", as all those scenes are recreated with dummies and props, and in the case of Chippin' Dale, about one hundred and fifty pounds of various red meats, plus three thousand bucks for the repairs needed to fix/clean the wood chipper afterwards.