Alan, I have spent a lot of time peering at the language on United's website about change fees, and have followed online discussions of the subject.
**Disclaimer: I am neither a lawyer nor an expert on the subject, just an interested observer. You will need to do your own homework and decide what's best for you. I believe United has some conflicting language on this subject on their various websites, making it less than crystal clear (as you have already observed).
That said, I think you can book with some confidence, at least within specific circumstances (below),
To cut to the chase: I think if you book your travel as a round trip (or multi-city trip), AND as long as the travel ORIGINATES in the US, you should not be charged a "change fee." You won't get a refund if you simply cancel, but you can change to a different/later flight and you should receive credit for what you paid.
If the flight you change to costs more, you will need to pay the difference; if the new flight costs less, you will receive FFC (future flight credit), not a refund. It also appears that you can keep "changing" the flight repeatedly if you want to just sit on the credit and use it later (but you won't get a refund); there appears to be no limit (at least none discovered and reported yet) to the number of times you can "change" your flight.
Where it would get sticky would be if you wanted to book two separate one-way tickets - one outbound, one return (the outbound would be eligible for no-change fees, but the return would not), or if you wanted to book a flight from Europe to the USA (one-way or round-trip). They clearly specify that only travel "originating" in the USA gets the no-change-fee credits. A round trip that starts in the USA would qualify.
Based on my reading of their rules, and also based on what I am seeing reported online, I believe the above to be true. No guarantees, but that's what I've seen. The firsthand reports of people since February 1 seem to confirm this.
Here's the critical bits on United's website: see United's website page, "No more change fees", and note the first paragraph (bolding is mine):
Enjoy more flexibility when you fly with us. We’ve permanently gotten rid of change fees for most Economy and premium cabin tickets for flights within the U.S., or between the U.S. and Mexico or the Caribbean. You also won’t pay change fees for international travel originating in the U.S.
The last 13 words seem pretty clear. I've got a screenshot, suggest you take one too. 😉
Hope that's useful. Good luck.