The video of yesterday's attempt would seem to prove the contrary. It remained relatively stable up until that leg slowly got loose and the rocket fell like a giant tree.
There are two problems with that view. First of all, it only is one landing. Maybe the next could be less favorable. Also the video also shows that the landing was still pretty rough. Just imagine the ship moving up during the final cm of landing and adding vertical velocity. Since it shortens the distance for the rocket to slow down, it could result in much higher landing velocity difference than just the speed of the platform.
Next problem, it could be that the legs could have been stable with a smoother landing, when a partial lock of the landing gear would be enough.
Also, "relatively stable" has a relatively different meaning when you are talking about a 46 meter high rocket stage. Even small differences, to small to be seen in a video, can already mean Meganewtons of force on critical connections. The Crawler of the Saturn V and Shuttle did not keep the rocket vertical within a fraction of a degree for aesthetics, it was really necessary to do that (and will remain necessary for the SLS)
If you look how helicopters land on ships, its really hard to imagine that the rocket stage should stay stable on deck with much less effort. Even if you include that the rocket will never operate during 7 meter waves. Helicopters are literally pressed against the deck until secured or in preparation of take-off, with the shock absorbers being compressed much more than possible by loading maximum cargo into it. And helicopters are generally much more favorable regarding their CG and landing gear layout