This claim states that chewing gum does not actually stay in your stomach for 7 years, as folklore suggests. I agree with this claim after researching the matter.
Chewing gum was created to be chewed, not swallowed, but it is generally not harmful if accidentally ingested. However, the gum is technically not digested. It is true that we cannot digest chewing gum, but it can move fairly easily through our digestive system and be excreted normally. On very rare occasions, very large amounts of gum swallowed have caused blockages in children.
https://www.mayoclinic.org/diseases-conditions/indigestion/expert-answers/digestive-system/faq-20058446
This information came from the Mayo Clinic, which is a very trusted and well-renowned source dedicated to health and medical information. They got their information from doctors.
According to Healthline, most of the components of gum can be safely digested. (sweeteners, flavors, preservatives). But, the gum base is what cannot be digested. However, your body can still safely pass gum in a normal amount of time.
https://www.healthline.com/health/how-long-does-gum-take-to-digest
I could not find any credible sources that had an argument that supported gum remaining in your system for more than a few days. So yes, your claim is correct!