ST Did Luke's lightsaber choose Rey or did she merely overpower Kylo?

A scene in TFA that has me intrigued is of course the epic moment when Luke's lightsaber flies pass Kylo and into Rey's hand.

So what just happened there? Was Rey simply stronger in the force in that moment? Did she just "piggyback" onto Kylo's force-pull, only to hijack it away from him at the last second? Or more intriguingly, did the lightsaber - and thus the force itself - display a clear preference for Rey? Was it Rey's doing or the lightsaber? If so, the light side of the force wanted Rey to have it then?

We've already seen examples in the movies of places having an allegiance for one side of the force or another (the cave on Dagobah). By that same line of thinking, is Luke's lightsaber then a instrument of or an embodiment of the light side of the force? It was the weapon of 2 Jedi's that were (mostly) associated with the light side during their career with it.

Earlier in TFA, it was shown that Luke's lightsaber was "charged" with the force (or at the very least used as an instrument or antenna by it), as the lightsaber was calling to Rey in Maz's basement, even opening a locked door for her.

What say you fellow fans? What's going on?