You're missing the concept of "vicarious liability", or "respondeat superior" if you want to get fancy-talkin', whereby an employer or organization on whose behalf you are acting is ultimately held liable for actions you take while in their employ or at their direction. This is the case in pretty much any Common Law country. It's also why the banks whose employees defrauded the market or sold their clients crap are ultimately the ones paying 8, 9, even 10 figures to settle charges by the authorities.
If the cook uses bad meat and you get gastritis, the restaurant (or the hotel, if it owns it) is held liable. The individual might be criminally liable on top of that, and/or might be held to partial account (e.g. by getting fired), but usually if you're an employee carrying out your duties in good faith, your employer is implicitly indemnifying you (holding you legally harmless and covering your ass) if you negligently screw something up. That doesn't apply if an injury is intentionally caused, of course, or if you were not acting in your capacity as an employee. But the USTA / NTC are almost certainly legally liable for the actions of their janitorial staff, whether they be contractors or employees.
(now, if the USTA uses a contractor service and the USTA is held liable, the USTA might sue that service to recover their settlement costs, so then you'd get into arguments over what the usual protocol was, who gave what orders to whom, etc... Let's hope we don't go down that rabbit-hole.)