Thinking more, I think there are good arguments for taking actions that as a by-product induce anthropic uncertainty; these are the standard hansonian situation where you build lots of ems of yourself to do bits of work then turn them off.
But I still don't agree with the people in the situation you describe because they're optimising over their own epistemic state, I think they're morally wrong to do that. I'm totally fine with a law requiring future governments to rebuild you / an em of you and give you a nice life (perhaps as a trade for working harder today to ensure that the future world exists), but that's conceptually analogous to extending your life, and doesn't require causing you to believe false things. You know you'll be turned off and then later a copy of you will be turned on, there's no anthropic uncertainty, you're just going to get lots of valuable stuff.
The comments here are a storage of not-posts and not-ideas that I would rather write down than not.