Requesting signature is about liability. The driver is supposed to get signature if you asked for it in the order. If they say they delivered the item and didn't get signature and the item is lost, they are going to have liability for it. If signature wasn't requested, then I believe the shipper may have liability, but it will more than likely be a debate about who is responsible.
I live in a safe area so usually don't ask unless the item is expensive. A watch would probably not hit that threshold. UPS is not the only one that does this. In the past when I lived in upstate NY, I ordered a $2,500 camera lens in the dead of winter, and had signature required, even though I work from a home office. It was well below freezing and I heard the truck and saw on the website that it was delivered.. I didn't sign anything. I believe this was DHL... it was a while ago. I went upstairs to get it out of the cold, and nothing was on my front porch. I called them and they contacted the driver... they lied about the situation and said he'd be there shortly. He had delivered it to the wrong house. About 15 minutes later I heard the truck again. I went upstairs and when I opened the door I saw the back of the truck as he drove away. I got the lens, but still no signature. I admit that after they acted, the thought crossed my mind to call them again and say I still don't have it and ask for verification of signature, but I've learned in life its better to let things go than cause trouble.
The bottom line is if you don't have the item and they can't show you proof of receipt with signature, they are on the hook for liability.