No. Your cell phone screen is showing what it's recording - a dark ride. Even you have the brightness cranked on it, you'd never know if someone was recording a video unless you specifically looked at another car, and even then, you are close to other cars for only split seconds during the ride.Sensible not only for the lost phone/hitting other passengers issue, but also because having a bright camera screen on in Space Mountain is particularly disruptive given the dark conditions.
I honestly understand the safety aspect of it, but like every other piece of safety legal wording in this country, this was implemented because someone did something they weren't supposed to. Example - "Do not attempt to consume Tide Pods."