I have a Nest camera. You're right, being in same VLAN does not give you access to video feed (at least via http). You need to view it online from their cloud.
Can you check if it is uploading a fixed or variable bitrate video? (Ie. does the bitrate change if there's no activity within the camera's FOV?)
Yes, the bit rate changes based on how much motion is in the cameras field of view.
It maxes out at about 1.5Mbps (1080p high motion)
Somehow having to access it from a Nest server, and hence have it be copied by Nest, does not inspire confidence. I'd be much more worried about someone looking at me via Nest than a burglar subverting my Nest camera.