I'm trying to book BEY-DXB on 31 August. For days, ITA Matrix has told me that it is much cheaper (about US$200) to book a round-trip ticket, such as BEY-DXB on 31 Aug and DXB-BEY on 19 Sep. It still does, and that fare shows up in search results on Orbitz, CheapoAir, and a few other sites, but when I click through to book it, the fare jumps to US$440 (and the one-way is $349 to $400).

Only the higher fares appear on Middle East Airlines' site, but they are marked as "Economy FullFlex" fares. When I click "Show fare comparison," I see, for refunds:

Refund before departure: 25 USD for Economy Super, Economy Saver, Economy Value, and Economy FullFlex
Refund after departure: Not possible for Economy Super or Economy Saver; 25 USD for Economy Value; free of charge for Economy FullFlex.

I don't understand this. Why would it be free to cancel a ticket after departure but $25 to cancel it before? Am I correct in thinking that if I book this ticket, I can cancel it before departure if something better comes along and receive all but $25 back?

And is there any trick to booking this seemingly phantom fare I see on ITA Matrix?

Sorry if this information is elsewhere; it is difficult to search for information on Middle East Airlines (since a search won't distinguish it from Middle East airlines in general), and using the code "ME" doesn't help either.

Seth