All the token balances could be calculated from transactions posted to Hive. Correct? Because all the tribes have their token issuance rules and whatnot documented in perfect detail?

Yeah that's the one decentralized thing about it.
In theory, balances could be recovered.

However the network can never be decentralized while these foolish miners are implemented using centralized random number generators. It's easy to see on-chain that Scotbot sent mining rewards to account at such&such time, but it's impossible to verify the legitimacy of the behind-the-scenes random number generator. The obvious solution is to eliminate the randomness of it and just pump out consistent ROI. Either that or you could use on-chain data as the seed for RNG.

In that case you could use witness signatures as a seed for RNG, but then that witness could cheat and give themselves the money. Or we could combine 21 blocks for a given seed so the only way to cheat is if all witnesses worked together to do it... which is obviously extremely unlikely.