This just doesn’t seem like an accurate description based on how blink has publicly described what makes their power management so impressive. If you are basing this conclusion off of something they have published, then please share it with us.
Although the sync module does obviously manage some communications between the cameras and the cloud, and in that sense could be described as the “brains” of the system I guess. But what @Estpaul has said seems much more consistent with what Blink staff themselves have publicly said, at least as far as power management.
Many of the exact details are of course a trade secret, which is apparently why amazon was willing to pay big bucks to acquire Blink.