Do I understand it right:
The chain doesn't store the state of my account, but the nodes calculate it, and I can query them for the balance - right? Then I only have the node's word for it, but I can test it by sending money to some other account. If my message is included in a block, then the previous balance is practically validated, and no more an assumption. Was this correct?
Right - this chain is a set of messages, where the other chains are a set of states (like UTXOs). To know the balance of your account, the node has to read all the relevant messages and calculate it.
In terms of a wider application, a blockchain typically relies on many miners or producers, and each of them can censor your messages, or in effect decline to process your transactions. But as there are many, your messages just pass on to the next and the next. So as long as most of the producers and you are in agreement over your total set of messages, your balance isn't in doubt.
Just sending another message such as a transfer does not validate directly your view of your balance - you'd have to instead transfer the lot to prove it. But with signed and agreed messages, it's a lot easier to write code that comes to solid consensus on a set of messages. In effect deviation is a bug. Bugs we can solve.