That is correct. In battlefields in World War I, the soil became rich with lime, poppies flourished, and it was that symbol, that flower, that a lot of the soldiers recall. Because of the commonality, the presence of the poppy during that time, it became identifiable as a symbol of remembrance, originating in France, being brought over to the United States and Canada back in 1921. Since that time, it has stood as our symbol of remembrance, and in fact it's been accepted internationally. So your thoughts are spot on; they are correct.
On October 6th, 2011. See this statement in context.