So what you're saying is something like...

Say you have some true preferences:

Heaventy

Nirvana

Populonopolous

Shitsville

Say you decide to list Populonopolous higher than Nirvana, even though you would ultimately like Nirvana better. There isn't space at Heaventy, so you are initially assigned to Populonopolous. This won't help you get into Nirvana, because you can't trade downward on your preference list. But as long as someone else got assigned to Heaventy that would have preferred Populonopolous, you could trade with them.