Yep, they assume you're not interested. USC said that they actually need to receive the deposit a few days BEFORE the deadline because it has to go through a few offices before it finally gets to the right people. USC does not have a "mailed by this date" policy. They actually have to have it in their hands on the date.
It's true and I guess that's why they usually send the new round of acceptance on January 8-10th because they already know if somebody is interested or not. Somebody who is interested in the school has already mailed the deposit.
Not all schools have a Jan 15 policy. I know that Stoybrook only has until Dec 30th. Be careful and make sure that you have the right date before you wait till the last minute to accept.