We have a velux on a very shallow pitch above the stairwell, and it has been fine, even in torrential rain. I am not saying the other guys were wrong, just that it doesn't have to leak necessarily.
The issues are likely to be with the flashing outside the room under the tiles. Check that it is turned up at the outer edges, so water can't be blown sideways past it, and that the corners around the window frame don't have holes or wrong-way-round overlaps. It's a while, but IIRC you are supposed to turn up the cut edges of the membrane up the sides of the frame under the flashing, so it may be leaking in higher up and running down on the membrane beside the frame, only becoming apparent at the bottom corner.
It is easy to get all this stuff wrong if you don't pay close attention when installing. Flashband will stick to the Velux aluminium flashing, so you can make good repairs with something a bit more durable than caulk. You used also to be able get a flashing kit separately, so you might redo it once the weather improves. You can reach pretty much everywhere you need to from the window, as long as you have good access inside.
My guess would be that someone made a mistake when installing it... hope you find something really obvious!
E.
