The HR VP is not holding the benefits administrators accountable for benefits related issues on paychecks. How should this be handled in a company level?
You might need to be more specific. I worked for a very large company you have all heard of as Disbursement Manager. Meaning I reported to Finance and payroll was one of my reporting groups. Very Senior Management was extremely clear that HR had nothing directly to do with payroll. That what ever payroll did and did not do was 100% on me. HR did not necessarily like that, but VSM could not care less. Payroll used to report to HR their, the I was hired as a direct result of a very ugly IRS audit. While HR liked making the decisions, they could not be bothered with making good decisions.
I worked closely with the Benefits Manger there. Made sure all of her questions and issues were addressed, if not necessarily to her satisfaction. But I have been payroll at several employers and never felt the need for HR to tell me what to do. I frequently felt the need to go over their head and have an adult make the decision.