Mostly right, with one correction. Gum base is a mix of ingredients, and many of them are synthetic polymers and resins, so "plastic and rubber" is a fair shorthand for much of it. But it isn't all plastic. Many brands also use natural materials such as waxes, resins and, in some gums, chicle.
The label says "gum base" because U.S. rules let a manufacturer use that one term for a blend of approved ingredients. The FDA list for gum base is in 21 CFR 172.615, and it's the right place to check the specific substances. I haven't verified the count of 46 that the post gives, so I wouldn't repeat that number without reading the regulation.
The part about not dissolving is also sound. The body doesn't break down the gum base polymer. Sweeteners and flavors dissolve or wear away while you chew, and the base is what remains. Whether gum base breaks down quickly in the environment is a separate question, and I haven't checked a study on it, so I can't say how long it lasts on a sidewalk. The chicle claim for Simply Gum and Glee is also something I haven't confirmed from their packaging.
