As I said, it could be several reasons.
Zeffy's photo is, I think, a Falcon, so let's take that.
Tail anhedral will reduce the aircraft rolling moment due to sideslip, which will change the balance between dutch roll and spiral stability a little bit. But unless someone can say that the Falcon is "iffy" in either of those quantities that is unlikely to be the reason.
In his book "JAR Professional Pilot Studies" Phil Croucher writes:
Anhedral reduces the lateral stability. In the Falcon, where it is used on the tailplane, it improves flying qualities by reducing the effect of wing downwash
Hope that helps