Surely in the vast majority of cases it's what people agreed was the arrangement that matters. I know tax considerations complicate this.
This case seems like basically every other contractor/employee status dispute, except turned on its head.
Normally, the company has tried to reclassify people who are morally employees as "contractors" to avoid the benefits and terms obligations that come with full-time employees. And no, despite what the "agreement" between the parties may have been, you can't simply call someone whose work obligations are structured identically to employees a "contractor"; companies routinely get dinged for trying to do this.