You should first and foremost check out DigitalRev TV's review of the Phantom 4. The guy took it off from a boat and a short while after that he said that the Phantom began matching the speed of the boat it took off from without any throttle input from the RC. After that, he tried landing it on the boat and it did very softly as if it was just landing on still ground.
Can anybody confirm if the Phantom or Mavic for this matter, can really do this stunt? Chris Rollins's Mavic fell of the truck he tried to land it on...

Yes, it's possible to take off and land from a moving vehicle or boat; it's not necessarily easy depending on various factors (speed and consistency of the movement, wind, etc.) but it's definitely possible with the Mavic.

I think it's possible in Atti mode, or better in Opti mode (with visual sensors enabled and GPS disabled).

There was this video of guys trying to land Mavic on a moving pick-up truck and failing spectacularly.

My friend did fly Phantom 3 from the boat. Taking off is easy. Landing was harder, he needed to match drone speed to the boat's. So he ended up hand catching Phantom. Mavic is a bit harder to hand catch, and I wouldn't risk doing so while moving horizonataly.

Having some sort of the landing net though...