It's more like floating the insurance company. The employer would never directly pay these things.

Most employers in the U.S. over about 1,000 employees are “self-insured”, meaning they hire the insurance company for the network and administration, but the company actually does directly pay out claims. At over 1k employees, I expect MailChimp was already self-insuring, and Intuit definitely does.

Intuit is indeed self-insured.