Thanks. Wasn't aware that every single node receiving a new block also checks the transactions in the new block. I assume each node also performs a "block message" (https://en.bitcoin.it/wiki/Protocol_rules#.22block.22_messages) check upon receiving new blocks.

Another thought occured: what if Eve changes her input to 1000 (of account A) and then send that 1000 to B. But this (https://en.bitcoin.it/wiki/Protocol_rules#.22block.22_messages) reads it becomes an orphan transaction, because there is no corresponding 'out' for Eve's 'input'.