This world has satellites that can detect flies from out of space, and they can't detect a huge boeing.

It's not so easy
As you get higher, you move slower, hence you can see a larger picture at once but move through the whole earth very slowly. At about 36k feet you move at the same speed as the earth's rotation and hence can only see one part of the world.
Communication satellites usually hang around about 36k, most spy satellites do too. But since it's so expensive to launch and maintain these satellites, they can only monitor parts of the world. That is, they can for example monitor washington or the kremlin, but they don't have enough satellites to view a remote part of the ocean.
The rest of the earth's picture come from polar satellites, which can see a very thin strip of the earth, come back and see another strip. Google earth's satellite works like that.
So even though you can technically see any part of the earth, you can't always see it at will. You can launch a high altitude satellite that can monitor parts that you really want to monitor, and use polar satellites to map the rest. There's absolutely no satellite system that can view any point on earth as it wants.
If someone is knowledgeable enough (And i mean scientific contacts, not necessarily military. You can probably map out the timings with wikipedia and a telescope. If you have military contacts then it's much easier) then they could time it such that it can sneak out of range.
This is why the SIA idea is credible, because if timed right the satellite would of very easily just snuck behind the SIA plane and nobody would of noticed. The hijacker (And it's safe to assume hijacking at this point, the actions on board the plane are clearly not natural) probably didn't plan for the UK communication satellite to pick up on him, but no spy satellite can easily track it.
Edit: Crowd search for MH 370. The colored regions are the photos the satellite has been able to snap so far
https://www.mapbox.com/labs/blackbridge/flight-mh370/#3/-4.48/137.11