I think that they activated the operating reverse as soon that they realized that they were on the ground, the plane was not flyable anymore and needed urgent braking by all means.
And I talking about a very big miscalculation of speeds. There is going to be hard to raise the nose and make the plane fly, but once it is in the air it becomes uncontrolable.
Another suspect is incorrect config Flaps/Slats, trim, spoilers, but in this case the config alarm should not be working, and this is very strange, because if you realize problems during the take off lift off and both engines are running normally, someone is going to look at the flaps, Spoilers, etc, and you will sense some kind of buffeting.
I bet that something very simple is behind this. 20-25 knot of speed error is enough to make this crash happen.
You wont notice it during the lift off because you will looking at abnormal config items or engine parameters. If your speeds are wrong and you dont notice it, everythings is going to appear normal, and you dont know what is really wrong with the plane.