My earlier posts are true within random definitions and overall I think that the game's random generator is good enough for general play. However there is no doubt that there are too many candy canes compared to the others. There must be some kind of weighting affecting one or the other.
Regardless I agree with the quoted post that there still should be enough to complete the achievements if that is the goal. It's unfortunate that it's not more balanced because that would allow for a few more lots of presents and also allow for some decent trading for players that are slightly ahead or behind on a particular item but there will be enough for the event completion.