Yes this is true, we are planning a trip in February, originally we were planning to fly out on the 13th. Because this starts peak season and would have had to pay rack rate for the vacation. We changed the trip so we will be flying out on the 12th. With an value rate and an AP discount we are saving over $1400.
One day can really make the difference in the price of your vacation. If it is at all possible try to leave on a value day even if it's the last day. You will save yourself a bundle of money.