If I had to do payroll, I'd probably try to find a SaaS that I could contractually lock to strict confidentiality. I wouldn't be in the business of saving pennies by selling out my employees' privacy.
This does not even remotely exist.
Getting anybody to do payroll for you means signing reams and reams of fine print where you absolve them, indemnify them, hold them harmless, and agree to bear their children. Well, maybe not the last part.
It's a nightmare.
It's somewhat expectable though. They're selling a service to people who don't want to deal with red tape (i.e. payroll) and read fine print (which is basically what doing your own payroll amounts to -- a lot of that). So their customer base is strongly self-selected for being susceptible to fine-print abuse.
For example, since many other small businesses use them, you may be paying your invoices through their payment portal for bills sent to you.
They've done deals with bill.com (which bought divvy for 2.5B).
Your payroll provider may provide payroll information to assist employees with their intuit turbotax filings.
Not paying them directly for services is very different than never engaging in transactions which involve something as a third-party. And it means this person isn't directly paying them to do anything.
I just took that to mean what they said and pointed out it's hard to avoid using these bigger players software.