FWIW here is the official text, taken from
https://www.united.com/web/en-US/app...romoCode=A5753
United's 24-hour flexible booking policy allows the flexibility to make changes to your reservations within 24 hours of purchasing your ticket, without incurring change fees. This includes canceling your reservation and requesting a 100% refund of the ticket price. Applies to tickets booked at united.com or with the United Customer Contact Center. The 24-hour timeframe begins at the time your ticket is purchased.
I'm not sure how this works for reservations made with the United Customer Contact Center, but reservations made at united.com afaik always require a ticket purchase at the end of the process (except FareLock), even if the resulting ticketing takes more than a day, and even if you elect to pay with cash or Western Union (note that "paying" is an obligation that follows after "purchasing" and they're not the same thing). This doesn't seem to be more liberal than the DOT regulation, instead it's exactly what the DOT requires.
As other posters noted above, UA seems to have a more liberal policy if you call in, but afaik that is unpublished policy and so can be taken away at any time without legal recourse. So if you really depend on this policy, cancel before the end of the 24-hour period starting when you click the big "PURCHASE" button.