There are charts from other Twitter peeps, PlanB, Woo-something ... if all ChartBuddy did was post numbers, there wouldn't be much to censor. That and Jack Dorsey runs a full node.
It's more a principled stand.
There are some apps that run on top of blockchains, so posts are immutable. One such is discussions.app
There are still moderators, but they are opt-in, simply to take care of any legal issues. Anyone can run a full node still and see everything.