I don't know how much stock I put into this. If you're going based off of what Yates said in that Reddit interview, I'd take that with a grain of salt. Palmer was working on a 3D head mounted display back in 2010/2011 and Valve has only admitted to VR research since 2012/2013. That's not to say that they couldn't have worked on it before then, but Palmer wasn't involved at that point. He also was only working on a 3D headset and wasn't initially planning on a VR headset from what I understand.
On top of that, Oculus definitely had more marketing/media buzz so they were ahead of Valve in the consumer mind. The end product might be closer to Valve's than to his original prototype, but he definitely had a small head start on them for the prototype and a huge head start from a marketing perspective. Valve all but shattered that.
Here's Palmer's first announcement in like 2012: http://www.mtbs3d.com/phpBB/viewtopic.php?f=140&t=14777