I can't be arsed looking back over all Everton's games this season, but the only highlights I've seen were v Bournemouth. I hate to say it but Walcott's goal can only be described as a pace goal (and maybe also a keeper mistake too).
Using Steve's criteria, as a pace goal it can't possibly count, so the 2-2 win becomes a 2-1 defeat.
Still, never mind, it's early in the season and points don't matter.