The specific truth is that the Fed has fewer constraints on its policy decisions than the Dept. of Education does.
The Dept. of Education's policy decisions are tightly constrained by Congress. If there's a law on the books giving the DoE freedom to determine student loan interest rates, then they can. I don't think such a law exists, though, so the Congress would need to pass one.
The Fed was created by Congress, and has a multi-part mission that it must meet, which has been set by Congress. But beyond that, it has great freedom to determine how to meet that mission on a day-to-day basis.
The Fed is part of the federal government, though. It even has its own federal police force.
The Dept. of Education's policy decisions are tightly constrained by Congress. If there's a law on the books giving the DoE freedom to determine student loan interest rates, then they can. I don't think such a law exists, though, so the Congress would need to pass one.
The Fed was created by Congress, and has a multi-part mission that it must meet, which has been set by Congress. But beyond that, it has great freedom to determine how to meet that mission on a day-to-day basis.
The Fed is part of the federal government, though. It even has its own federal police force.