Earlier quoted context omitted.
I would suspect you would not be considered an employee but a contractor. I am not sure how they much they're required to report about their vendors.
In the US and comparable jurisdictions, the concept of employee and contractor are not interchangeable and imply differences in things like autonomy and expectations. This is as much to make sure that workers have appropriate protections and that contractors have appropriate freedom as it is about tax reporting or whatever. Far more likely is that these companies aren't well-footed legally and don't realize that they…
Plenty of contractors are basically employees paying less taxes and not having holidays.
(not that I'm complaining, I'm glad there is a legal way to minimise how much the government steals from me)
States are a bit trickier because healthcare is so ridiculously overpriced and therefore people value health insurance provided by an employer. I never even bothered to sign up for the private health insurance I had in the UK and just either user the crappy public one or paid out of pocket, finding the best doctor for the job (instead of what my insurance would have offered).