I skipped reading the article, as I thought there was no way MI6 existed in 1916 when Rasputin died. But just to be fair I decided to Wikipedia it - and discovered it was founded in 1909 https://en.m.wikipedia.org/wiki/Secret_Intelligence_Service
The idea is not a new one - Oswald Rayner's wikipedia entry, for example, mentions his involvement in the plot, or just google Rasputin and Rayner. It's going a bit further to look at MI6 as instigators or knowing collaborators, of course, but it would have been terribly remiss of Rayner, then in their employ, to go about assisting in murders of national figures without seeking approval.
My one fatal flaw to this whole idea was so what. Almost everyone wanted the man dead except for the Mr. and Mrs. Romanov. He was incredibly influential crazy man who scared everyone.
If this really bothers people I think ignorance will help you to sleep at night because I am sure this happens MUCH more than anyone cares to figure.
Plus we wouldn't have the most amazing story of how Rasputin died. That story scares me every time I read it. Shot, poisoned enough to kill a person multiple of times over and he dies from drowning when they threw his body over into the river inside a rug.
So now I'm off to read the article.