None of the secretaries have direct control or authority over the OPM.
Additionally, the Secretary of State is foreign affairs and not the equivalent of the Home Secretary.
https://en.wikipedia.org/wiki/Katherine_Archuleta
That is the person who is responsible for the OPM.
It operates on a fee-for-service model for 90% of its budget and isn't properly funding IT and IT security. Given she has only been there 18 months, I'm not sure how you can really blame her beyond the fact she didn't follow the "shutdown and repair" recommendation...except for the fact if she did that, she'd have to burn through the OPM's cash reserves as the only way to fund it.
Its honestly more of a flaw in the way Congress built the OPM incentive structure and the fact the director is a revolving door position that changes every 2-4 years.
The government simply just doesn't fund/prioritize IT & IT security properly outside of the intelligence services. They also build these psuedo-private-sector funding models that create the incentive to "ignore" cost centers like Security into critical infrastructure like the OPM. Its really horrific.