Yes, each license key would be unique to each customer, as well as having limits on it for what features, capacity, etc. the license supports.
It depends on how they bought VMware licenses in the past if things have to check in. Some channels of licenses you had to run Usage Meter on, some you didn't. While there is an offline feature of Usage Meter, it was hardly allowed ever. Other channels of licenses did not call back to the home office. and it was trusted with audit backup that everything was deployed and conformed correctly. The core products do not contact back to VMware, only Usage Meter. (Two software sets that do connect back directly are AVI Load Balancer, and now vDefend FW).
One thing that Broadcom has made very clear is that it is against the terms of the license that you cannot patch/upgrade perpetual licenses without subscription support services on it.
Large corporations must run full patched software for terms of compliance (ie. in order to even get cyber insurance you would have to prove to be fully up to date and patched).
If an audit turns up your perpetual software licenses with expired subscription services have patches applied that were released past the subscription expiration date, the company would be on the hook for catching up and paying for all subscription support services. Since patching is pretty much a requirement, this patching often went on and nobody wants to pay subscription support fees, so that was frequently dropped.
Most likely this scenario described in the story was smoke screen to hide that they abused patches so they didn't have to catch up and pay Broadcom for their true usage.
Also, it could be they claim to have shut off all services, but they continue to run in the backend without Broadcom knowing any better, because they turned off Usage Meter, and claim an audit won't find anything. Its not like an auditor drives to the data centers, and physically tally every machine they find within it.
Yes the latest Broadcom version of the VMware software changes the license model. All software is required to call and check in and will disconnect your hosts if your subscription license isn't valid and up to date.