Why does the Falcon 900 have anhedral wings?
For the same reason why the Lockheed F-104 Starfighter had such a pronounced anhedral: It is the size and location of the vertical tail.



Lockheed F-104 Starfighter (picture source).

In both cases, the vertical tail is large relative to the wing and fully above the roll axis. In a sideslip it produces a high rolling moment, so any more rolling moment from the wing would reduce the handling qualities of the aircraft.

Especially in case of the F-104, the raised position of the horizontal tail shifts the center of pressure on the vertical tail upwards, exacerbating the offset location of the vertical tail.

The rear-mounted engines on the Falcon 900 move the center of gravity backwards, so the wing is more backwards than usual for aircraft with wing-mounted engines. Therefore, the part of the fuselage ahead of the center of gravity is large, requiring a larger vertical tail to overcome the destabilizing yawing moment of the fuselage.

The same is true for the Tupolev 134 and 154, and - surprise! - they also have no dihedral, even though both are low-wing configurations.



Tupolev 154M of the Polish Air Force (picture source)