You would have done well to have read the first paragraph of the linked article in the OP:
Legislative definitions of an
agency of the
federal government of the United States are varied, and even contradictory. The official
United States Government Manual offers no definition.
[1][2] While the Administrative Procedure Act definition of "agency" applies to most executive branch agencies,
Congress may define an agency however it chooses in enabling legislation, and through subsequent litigation often involving the Freedom of Information Act and the
Government in the Sunshine Act. These further cloud attempts to enumerate a list of agencies.
[3][4]
The first link within that link provides even deeper insight to rebut your bare assertion:
A
government agency or
state agency, sometimes an
appointed commission, is a permanent or semi-permanent
organization in the
machinery of government (
bureaucracy) that is responsible for the oversight and administration of specific functions, such as an administration.
[1] There is a notable variety of agency types. Although usage differs, a government agency is normally distinct both from a department or ministry, and other types of public body established by
government. The functions of an agency are normally executive in character since different types of organizations (
such as commissions) are most often constituted in an advisory role — this distinction is often blurred in practice however, it is not allowed.
en.wikipedia.org