You're right, but only by default.

Google forgoes DoD funding once they acquire companies which :

1) have already received DoD funding/grants

2) already have contracts in place with the DoD that must be honored post-acquisition, but are contractually in name with the previous vendor, using Google only as the global representative of the previous existent vendor, while reaping the benefits of a contract.

So, Google surely won't create SkyNet. But 'Cyberdyne Systems : a Google Company' probably will.