Yes it's true. Gum base is made from various polymers and plastics, either synthetic or naturally extracted from plants. Regardless of whether it's natural or synthetic, some microparticles will strip off into your saliva during chewing and enter your digestive tract. The vast majority of this will pass all the way through your digestive system without ever being absorbed into your bloodstream. But there may be nanoparticles small enough to pass through your gut membranes into your bloodstream.

The amount that gets absorbed is unknown, as are the long term affects of this. It's clearly not dangerous in the short term, else billions would be sick all the time from chewing gum. But more science needs to be done to fully understand the implications of this.

As for alternatives, altoids are a particularly strong mint that lasts, imo. But if mints aren't your jam, you can always keep a small bottle of mouth wash with you to get an occasional swish from (be careful not to dry your mouth out with it, or that will make your breath and oral health worse) and dissolvable breath strips if you can find them (feels like they're nowhere near as common as they where when I was a kid). Also proper oral hygiene including twice daily tongue brushing/scraping keeps your breathe from getting bad in the first place, even if it's not actually minty from that.