This obfuscation of who works for who via a series of subcontracts is horrible. I personally know of the janitorial BS that got started by Winters Cleaning and the cinema industry in the 90s. There's an article that Variety did on it some years back. It's about removing responsibility from the company benefitting from the labor. It increases the likelihood that impoverished, desperate people will be taken advantage of. When problems are noticed the last company in the line of subcontractors just fold up. No one is held accountable.
If Amazon has deep control of operations due their contracts, then yes, Amazon is their employer.
Curious if someone in an abusive relationship could use this trick if their phone was being monitored. If the abuser was just monitoring them with the phone's parental controls this would work but if there was an app probably not?