Why exactly? They are talking at the individual employee level, not company wide. The statement above is: "[As an individual developer] it is ok to make mistakes, just own up to them and take responsibility."
They didn't touch on test coverage, integration Vs. unit testing, code reviews, UI automated testing, code quality inspections (both automated and manual), regression testing, external audits, or a whole bunch of other things a company can do to improve the quality of their software over the medium to long term. These exist to help mitigate an individual's errors.
If we take what you said above at face value, you're essentially saying: "It is unacceptable for an individual employee at a company who manages benefits to make mistakes ever period." Which when re-phased like that is patently absurd.
Your anecdotes above may be legitimate reasons to gripe about the quality of Zenefits' software. But these are issues with organisational quality, not individual quality. Individuals can and will make mistakes at any endeavour no matter how mission or life critical, the way organisations detect and resolve these mistakes is what is key to quality, not pretending that people should be mistake free, that's a pipe dream.