If your distributed database doesn't store all the transactions that have occurred...
Then how can anyone verify that the balance at an account is valid?
It's not that transactions aren't stored in the blockchain (they still are), it's just that they no longer reference other transactions in the blockchain, but rather they reference accounts (unique output scripts) in the UTXO set. When we parse the blockchain, we need to keep a UTXO set anyway, because an outpoint can only be redeemed once. This means we need to maintain a UTXO set in any case, and if transactions referenced this directly we could save space.
So only transaction inputs would change, nothing else.
EDIT: I've changed the title of the post to better reflect the above explanation, as I see how your doubt can arise when I say that the blockchain is "account-based" (it's the transactions, in the blockchain, that are account-based, so to speak).