I don't know what Google's contracts and agreements are with local municipality, so the short version of my answer is that I don't know how i'd classify Google Fiber myself.

For a more general point of view, i'd take into account a lot of factors such as:

- who "owns" the service, both from an "on paper" POV and who builds and maintains it

- what does the contracts between the entity and the government say

- did the government pay for a service to be built by the entity, vs the entity asked for permission to build the service, vs the entity built the service using non-government-permission-required resources

- what was the spirit of the relationship between the entity and the government

- who will be using the service

- is the service a government-allowed monopoly

- etc.

Facebook does pass some of those tests (eg. the "public at large" is the target userbase for it), but fail a lot of the other tests at least in how they operate in the United States. Comcast's general laying out of wire + offering services over that wire passes a lot more of those tests and puts the service into public infrastructure in most folks' eyes.

edit: formatting