They can, but they are subject to the same laws regarding mail fraud as the USPS. That puts them under the jurisdiction of DHS (and Secret Service).
"The term mail fraud refers to any scheme carried out in a fraudulent manner, with the intent of depriving another person of his or her property, or “honest services,” via the U.S. Postal Service, or any other interstate mail carrier. Since 1872, the crime of mail fraud has been classified as a federal offense in the United States, and carries serious penalties. To explore this concept, consider the following mail fraud definition." Source: LegalDictionary.net
UPS is an interstate mail carrier.