It is true that your body can not digest the gum. Apparently, rubber gum passes through your body just like any other type of food but is harder to digest.
The gastrointestinal tract is very strong if it can digest a tough steak it can digest gum.
The gastric movements , acids and enzymes available to break down gum but the base does not dissolved completely, because of its chemical properties.
It does not get dissolved into the small intestine unlike other foods, but still, the gum will be digested by the body.
The myth that gum would stick to your insides intestines the same way it would cling on any other object is not possible,the gum will just go out like everything else.
The gum would only be stuck if it was too large to fit through the opening of your stomach, but that would require chowing down on an enormous amount.
Reason to why it is not advised to chew gum is because it has absolutely no nutritional value so that's why its not advisable to swallow it. Gum won't harm or kill you but it is not good to swallow it purposefully.
Swallowing a big cud of gum could cause you to choke if it got caught in the windpipe, but this is still the same as any other type of food.