My guess is there might be an immigration problem as well. Just a hunch. And, besides payroll taxes, there's worker's comp, social security withholding and matching, disability insurance, liability insurance etc. etc. etc.
The regulations and requirments to employing anyone are cumbersome. So cumbersome in fact, that the people who make them so way are dissuading from actually following them.
All true (I have an LLM in taxation), however, there are ways to make it more likely that taxes and regs will be followed. I'm sure the Kennedys have a number of staff people. They could set up a company, with staff as employees. They could lease staff through an employment agency or any one of a number of companies set up to hire employees so organizations don't have to deal with the red tape.
Truth is, they didn't pay because the rules don't matter for them. You and I would be jacked up by the IRS for years.