I've seen it on products that do not possibly possess any of these non-nutrients. Sometimes they are, sometimes they are not. In order to truly know, you have to read the ingredients list.
If there are partially-hydrogenated oils or "shortening," then there is no trans fat in the food.
Saturated fat in trace amounts is not a big deal. It's not actually a huge problem in larger quantities either, as long as one does not go overboard with it.
With gum specifically, you definitely want to look out for trans fat, sugar alcohols (sucrulose, aspartame, etc), food dyes (these don't show up on nutrition facts, but they are definiitely something to avoid) and other preservatives.