Thinking about it more this story smells. They're clearly not being truthful about some part. If it was a remote controlled laptop from Arizona the time between a keystroke on the laptop and Amazon receiving it should be normal.

If the remote controlled laptop part is true that would be because Amazon only allows company issued devices to access the VPN (and then access internal resources) which lines up with my experience. To get around that and not have to use the corp laptop they would have to crack whatever secure endpoint attestation Amazon is using to connect to the VPN. Then they'd have to reverse engineer and spoof all the spyware (that's doing shit like apparently precisely tracking every keystroke). Because without the spyware checking in reporting normal they'd probably detect it even faster. After that's done you're right they'd obviously want to use a proxy but again that doesn't seem at all why they were caught and getting to the point of being able to just directly connect to Amazon's VPN through a proxy would be a heavy lift requiring a very sophisticated attacker.

The corporate laptop is probably very locked down and I bet Amazon actually caught this from the remote control software being detected by some local security scanner that wasn't properly circumvented.