No it's not 100% false, it's about 70% correct, refunds are in (expiring, non-transferable) flight credits not money-back. The preceding poster said "your money back" not "flight credits".
Flight credits expire (with US carriers, typically in 12 months, sometimes within only 3 months (Spirit), with European carriers, sometimes up to 3 years), and cannot be transferred to any other passenger [0], unlike even airmiles; and using them with partner airlines can be restricted; many passengers are unaware of much of that and airlines do not point it out, and rely on the fact that passengers may not realize till the credit has expired.
(In 7/2022, Southwest did uniquely eliminate expiration on flight credits unexpired from July 28, 2022 onward.)
Just because an airline only initially offers (restricted, expiring) travel credits, doesn't mean much; in some cases [1] passengers may be entitled to an actual money-back refund: (a) canceled flight b) passenger has documented medical circumstance c) cancellations due to Covid d) possibly other circumstance).
One excellent advocacy resource is [2] Elliott.org 12/2022: "The complete guide to using your airline flight credit now".
EU regulations are more pro-passenger than USDOT.
Southwest in 3/2022 unveiled its long-awaited new fare category "Wanna Get Away Plus" whose key perk is the ability to transfer flight credits, which Southwest calls travel funds (which sounds like intentionally misleading language, but anyway). But again, SW charge more for WGA+.
> Southwest Airlines... refund policy for refundable flights is a full refund up to 10 mins before the flight.
But that's the minority case: only Southwest's Anytime and higher fares are (money-back-)refundable, and they are typically way more expensive (2.5-4x) than non-refundable WGA fares. I can't find data but AFAIK most SW non-business passengers are WGA fares.
So the statement:
>> Tickets are nonrefundable because otherwise the network doesn't work, financially.
is in the general case true.
(One well-known travel hack with SWA for frequent travelers who didn't know their departure dates 3 weeks in advance used to be to buy 3+ different non-refundable tickets spaced out by say a week each, then refund whichever tickets you didn't end up needing. This was still cheaper than one Anytime fare.)
[0]: https://www.usatoday.com/story/travel/airline-news/2022/03/2...
[1]: https://www.usatoday.com/story/travel/advice/2020/10/09/flig...
[2]: https://www.elliott.org/ultimate-consumer-guides-smart-trave...