He also mentions he's on a corp-to-corp arrangement, which means the "employer" is invoiced by the "employee"'s company.

The pay is likely going to an LLC via its EIN rather than to a person (him/her) via his/her SSN.

Some companies, Google being one of them, allow you to opt-out of sharing any data with Equifax. Perhaps there's a more 'global' way to prevent that data sharing, too