The part about the "others" isn't really true. Paul and Robert had founded two companies together and Paul had been the CEO of a medium sized startup and taken it through the acquisition process.
Also, at least in the earlier YC batches before there were more folks helping out, Jessica definitely felt like the operations person; like she was the one that actually made things happen.
We are talking about the same thing. I meant operations as part of legal/financial -- the business side of things. As Paul put it in an interview at Mixergy.com, she brought the knowledge required to actually put YCombinator together. I certainly meant no knock on the other partners' experience other than what they claimed to lack themselves.
Also, at least in the earlier YC batches before there were more folks helping out, Jessica definitely felt like the operations person; like she was the one that actually made things happen.