As others have said, it's not so much that UPS knows this, but that they subscribe to a service that aggregates this kind of data. Go get your credit report online. You'll be asked similar questions. Do credit reporting agencies know this data? Not necessarily, they subscribe to a service that aggregates it so they can confirm the person trying to get your credit report is you.

UPS has, unfortunately, been quite the unintended accessory of credit card fraud/identity theft. I worked for a company that lost $30,000 to credit card fraud in a single month. Almost exclusively, the perpetrators would order $500+ in merchandise and have it Next Day Delivered to a vacant (but legal) address. Once they got the tracking number, they called UPS and had it rerouted for pickup. UPS says they check driver's licenses for pickup, but obviously this policy is inconsistently applied.

In reaction, the company I worked for modified its UPS contract to disallow reroutes. This caused an amazing number of headaches for the company's customer service staff and for UPS customer service, as many legitimate customers were caught in this net intended to prevent fraud loss. Most of my experience with UPS comes via my former company. As a mere consumer of UPS services nowadays, I've noticed a number of service improvements that I remember my previous company suffering from previously. It's interesting.