"I would think that military systems are watching EVERYTHING".
No. They are not. Your average commuter airport needs dozens of people just to understands the situation for day to day stuff, let alone secretly watching from afar and trying to get a grasp on why one plane moved. There's a reason that air traffic control also control military aircraft manoeuvres to some extent too.
This is the point - if there were so many people watching, from so many countries, so perfectly, with equipment that performs your impossible miracles, then there are dozens of countries who would happily stand up and say "We saw something suspicious" because they could accuse their enemies. Fact is, nobody has.
So it's either a global conspiracy with perfect equipment, totalitarian surveillance, absolute collusion and everyone knows this. Or we just don't do that kind of stuff. And we don't.
One country's military doesn't care about anything except something which isn't on its registered flightpath within their airspace (which they are normally notified OF, not notice themselves), or something that doesn't appear with a registered flightpath at all.
Flying out into international waters is of no concern to the military of a particular country whatsoever. They have control only up to a limit from the boundary and no more and although they can survey outside that and often do (which is how the UK often spots Russian aircraft approaching its airspace, they are constantly testing but nowhere near stupid enough to actually violate it) they cannot do anything until it's in their territory - and then they have 100 miles in which to see it and get it. Some plane detouring could be anything from a drunk on board to airline recalling an empty aircraft to help with a schedule change.
And outside of that national boundary, literally nobody cares. There are no laws out there, there is no ownership out there, and thousands of planes (and ships!) come and go and change flight plans every day and do not notify every damn country in the world of themselves doing so. It only matters when you enter an airspace without a flightplan or deviate from one inside it.
If what you said was true, the Bermuda Triangle would not have the reputation it does, you wouldn't get helicopters being landed on top of protected-sites like wildlife reserves, the military would be first on the scene in a crash, etc.
Occam's razor. Either everything is absolutely perfect except for the something extraordinary that happened in front of the world's press involving convoluted conspiracy theories, or things just don't operate like you imagine they do.