Short answer: no. It isn’t. Some statutes, and the IDEA is one of them, set forth what the government wants to have done and establishes an agency that specializes in the issue involved. Lawyers call these departments “administrative agencies.” Administrative proceedings are not lawsuits. Lawyers call them “quasi-judicial” (in other words, kind of, sort of).
The Federal agency responsible for oversight of the IDEA is the United States Department of Education Office of Special Education and Rehabilitative Services. However, the IDEA is a grant of funds to the states and requires that states enact rules implementing the IDEA. This is done through the education departments of the respective states, whose rules are reviewed and approved by the U.S. Department of Education. State agencies are empowered to resolve disputes in “administrative proceedings.” The due process or impartial hearing proceeding is called an “administrative proceeding.”
Some states, like New York, have a two-tiered hearing system. In New York, the first hearing is before an “impartial hearing officer.” The impartial hearing officer can administer oaths and issue subpoenas requiring witnesses to appear at the hearing. Their decision is binding unless one party appeals. In New York, appeal can be taken to the State Review Officer. Beyond that, appeal can be taken to either the state or federal court. State courts and federal courts exist because of the state and federal constitutions, respectively. In state or federal court, cases are heard and decided by judges, not hearing officers and different rules and procedures apply in state and federal court that do not apply in the administrative proceeding.