Postscript: 1/3/15. This quote has been niggling at me for the last three months. I've finally got back to doing some more Internet mining, and have come up with a published source which directly links it to Milne. This quote does indeed appear in an essay by Milne entitled "Intellectual Snobbery", which probably first appeared in the magazine Punch (although I can't quite confirm the exact year, issue, and page number) but which definitely appeared in a collection of Milne essays entitled "Not That It Matters" (published 1920) - a free copy of which can be download from the Project Gutenburg website. It was also reproduced in the American magazine Littell's Living Age (published August 23, 1919, p. 462-463), a full pdf of which can be sourced here.
So definitely Milne; definitely not Pooh. Phew! Now I can sleep again.