I think there are several angles to look at this, and a lot of it revolves around your definition of knighthood... and that part can be a bit sticky, since you have to ask "what century and which country?"
To be a modern knight in a country that still has knighthoods, then it simply must be bestowed by the governing body there. In the UK, you're a knight when the queen knights you.
Historical knighthood doesn't exist anymore, since we're removed from it by several centuries. No one can be a 13th Century knight, for instance, because it is now the 21st century.
However, I don't see an issue with historical recreations that depict knights. Nor do I see a problem with private organizations (Orders, the SCA, etc) having their own version of it. Is it the same thing? No, of course not. It's a different interpretation.
And while the accolade will come from an external source, you don't need a tap on the shoulders to be chivalrous. Arguably, you must be knightly first, before you will be knighted by someone. Or in the case of the UK, you just need to be very successful or famous.
Knighthood and chivalry have evolved so much over the centuries that the later versions show very little resemblance to the earlier versions.
I certainly understand where he's coming from. But I don't see the point of railing on private organizations, especially if they're historical recreations, or hobbies. True, not everyone is going to get their facts straight. There are still many misconceptions out there.
So to me, there are many forms of knighthood today. And I don't have any trouble or conflict in keeping them all in my brain at once. I think it's OK to have historical recreations, private clubs, private Orders, hobbyists, and so on, alive and well today in addition to the living tradition of knighthood that still exists in only a small number of countries. I don't see these things as mutually exclusive.