I disagree with your analogy. Obama's job concerned way more things than the OPM. However, it was Katherine Archuleta's only job to lead that organization. When considering the OPM only, Archuleta was much more akin to the CEO than Obama was.

I think a more appropriate analogy would be that Obama was the "board of directors" of the OPM.

OPM isn't an complete organization. It doesn't have a mission that makes any sense independent of the rest of the federal government. It only makes sense as a department serving as part of larger organization. Like HR or IT in a particular company.

Equifax on the other hand is a complete organization. It has a bunch of different departments that all work together to accomplish the overall goal. Just like OPM, the State Department, and the Treasury all work together to accomplish the overall goal of governing the nation.

Therefore, the proper analogy for Equifax is the USG, not OPM, and the proper analogy for Equifax's CEO is Obama, not Archuleta. The group that is analogous to the Equifax Board of Directors is Congress.

I see your point with the OPM. Your analogy is logically consistent, but I still don't find it to be realistic.

Equifax fits into the relatively tidy box of credit reporting, identity theft protection, and maybe a few other services that I missed. The OPM fits into the relatively tidy box of investigating and managing security clearances, hiring Administrative Law Judges, and maybe a few other services that I missed. I can't even reasonably estimate the number of these services (to the same level of granularity) that the entire USG is responsible for.

Getting rid of the business structure analogy, really I just disagree with the sentiment that Obama should have been fired or pressured to resign over the OPM hack. I don't think there is much to be discussed there, so perhaps we should agree to disagree.