Yes that is absolutely true and an advantage over btc mixers would be that the mixer logs would be useless since the mixer itself wouldn't know where the coins came from. With a coinjoin-style mixer the mixer wouldn't even need to know where the coins are going either. With the former you still have the usual issue of the mixer stealing your coins and with the latter you have a simultaneity requirement and timing attacks (as with regular coinjoin). The denominations naturally used in Monero would help with some of the other coinjoin weaknesses (relationships between inputs and output values).
This would provide protection against the threat that someday the "crypto is cracked" and anonymity broken. But then again in the normal course of transactions through merchants, p2p transactions, loans, gambling, etc. there is a lot of natural mixing too.
You can easily add off-chain mixing to a coin that provides on-chain mixing but you can't easily do the opposite.
EDIT: I guess you could pre-derive a one-time destination address even with a receive-and-send mixer, which would remove the recipient address from the mixer's logs too. Currently there is no tooling to send to a precomputed one-time address but I don't see a reason why it couldn't work. Also, I guess there are some issues with r being per-tx not per-output, although I suppose that could be changed to enable this, at the cost of some added space.