Your understanding is close.
If I had 51%, I could mine a chain of blocks in which I transfer all my coins to my personal wallet. I'd mine this chain about 10 long, but not tell the rest of the network. At the same time, I convert all my coins to dollars on the exchange and withdraw them. This happens on the normal blockchain.

After my withdrawal has gone through. the normal blockchain is about 9 long, while my blockchain is 10 long. I announce all my blocks to the network, and lo and behold, the network confirms I am right.

But dollars can't be reverted! So the exchange takes a loss.


Instead of the exchange, I could do this with buying anything for bitcoins. If this happens a few times, it will probably kill bitcoin, or at least hurt the trust in the system severely.