If it’s any consolation, I’ve never been able to book cheap fares with MU directly.
We travelled with them last year (London to Tokyo via Shanghai) during the Easter Holidays having found an amazing price - £1,150 for three of us (2 adults and a 9 year old), but the only way to secure it was via an online travel agent (OTA)
The enormous downside with using an OTA was that when the inevitable schedule change occurred there was no way to contact anyone at the OTA to renegotiate flights or flight times. OTAs that were previously accessible are becoming harder to reach after ticket purchase, either through changes in policies or ownership (usually both). Luckily it worked out for us, but it was a sobering experience, it could so easily have turned into a nightmare.

Also (back in 2016) bought very cheap MU tickets for Mr LapLap to join us in Tokyo but he had to get a coach from Victoria to CDG on Good Friday in order to catch it (gridlock hell on the roads meant the coach missed its Eurotunnel slot and diverted to a ferry route, he made the flight by a whisker). Again, there was no way to buy this direct with MU, flight was £356 for travel 6 weeks later. Sure, we got to spend our 10 year wedding anniversary together but not something to be repeated.

In short, that fare you saw MIGHT have been available through an OTA, but buying it this way could have left you quite vulnerable.

In contrast - we booked with CA directly for our upcoming Easter trip, a big schedule change happened, we called CA and benefitted from the changes nicely (securing more convenient flights that had been out of our price range)