IOTA can prove it doesnt work at any time by removing the centralized servers known as the Coordinator which is otherwise enforcing the convergence of the chain.
Exactly, that's the problem. With Byteball there is a similar problem - it seems not to work without trusted "witnesses". However, there is no proof that it
doesn't work, so I give it a minimal chance.
For Byteball, each witness does not have to be trusted, only a majority of witnesses, users have to trust majority of witnesses would not collude or conspire - if they do that, the worst they can do is stall the network or prevent their replacement. Similar to bitcoin users trusting small group of miners or that a single miner would not be able to achieve majority.