This is docker-specific, obviously. Also, AFAICT it's not really 'deterministic builds' despite claims to the contrary since the network is allowed as input.
The first point is technically untrue - it works over ssh or plain bash also.
The second point is correct; it's deterministic in the sense that the ordering is always the same, and as much as Dockerfile are (they're also regularly described as deterministic). I should probably clarify that somewhere.