Changing your flight within 24 hours of purchasing it is different than changing to a flight within 24 hours of the original.

The latter doesn't need to happen within 24 hours of purchase.

As others have noted, this is not the same thing.

What the parent was talking about is usually called "same-day change" (abbreviated "SDC"), and is in fact only available free of charge to passengers who have a minimum status level within the frequent-flyer program.

Another related perk is the "guaranteed seat" -- the ability to purchase a ticket within 24 hours of the flight, and receive a guarantee that you will have a seat and will not be "bumped" due to overbooking (they'll bump someone else off the flight instead, if it comes to that). Which tends to kick in at the higher status tiers; back in my days of flying too much, I only used that perk once, and the last-minute ticket was expensive, but it was worth it to know I would get where I was going.

He's talking about 24 hours before the flight takes place. The 24 hr rule for purchases is us law.