"The head of each Federal agency shall make and preserve records containing adequate and proper documentation of the organization, functions, policies, decisions, procedures, and essential transactions of the agency and designed to furnish the information necessary to protect the legal and financial rights of the Government and of persons directly affected by the agency’s activities. (44 U.S. Code § 3101)"
The only relevant question is, "are emails 'records'?", and according to the State Department, the answer is yes:
"All employees must be aware that some of the variety of the messages being exchanged on E-mail are important to the Department and must be preserved; such messages are considered Federal records under the law. (5 FAM [Foreign Affairs Manual] "
And I might add that the accusation here is not that she had a personal account in addition to her official one, it's that she didn't have an official one at all.