Counterfeiting investigations are part of what the Secret Service does, it was actually the agency's primary function from when it was founded in 1865. The Secret Service wasn't tasked with protecting US presidents, their families, foreign dignitaries and other important figures in US government until 1901, presumably following the assassination of then-president William McKinley.
Horrigan, likely because of his (fictional) involvement in the death of John Kennedy in 1963, was reassigned to the counterfeiting section or he could have requested that transfer due to being so traumatized by the incident.