I don't think there is any truth in that saying. That saying applies to cats (mostly). I've had a dog for about 6 years now and we have always been changing his food and he has never had problems due to that.

Also take a look at : [How often should i change dog foods?][1]. It says here that dog foods can be changed every 3 months.

As [salketer said:][2]

> I'm sure the food companies have a part to play in this [...]


  [1]: http://www.dogfoodanalysis.com/how-often-should-i-change-foods.html
  [2]: https://pets.stackexchange.com/questions/427/is-there-truth-to-the-idea-that-changing-food-too-often-make-your-dog-sick#comment557_427