There's no way to prove that in a quantifiable way, IMO, because there are many possible drivers for price appreciation. Now, it's generally accepted in the field of economics that additional demand in the face of unchanging supply leads to higher prices in unregulated capital markets, but its hard to characterize exactly how much additional demand is created by the hdbstabilizer on a relative basis (mainly because it's fairly clear that a lot of reported volume on some centralized exchanges is not real).

But what is quite provable is that the DHF, which funds a lot of development for the Hive ecosystem, is profiting substantially from the stabilizer (which in turn means the cost to the blockchain of all that development is lower). From my point of view as a Hive holder, that's good enough.