Even the federal government is apparently paying too much for EpiPens, along with angry patients and insurers.

The skyrocketing price of the life-saving allergy shot, which has triggered a storm of criticism, is only part of the problem. Now the federal government, responding to Congressional inquiries, says Medicaid has for years been paying too much for EpiPens because the emergency shot is classified incorrectly as a generic medicine.

The federal government says EpiPen is a branded drug, which means the drug's maker, Mylan, should have been paying the government a far higher rebate under the government's complex pricing rules. Mylan could face steep penalties.

Mylan, which has been blasted for hiking EpiPen's price to $608 from $94 since 2007, denies wrongdoing.