That's not how a VPN works. A VPN masks the information you are actually accessing by showing you query the VPN instead. To make a connection to a service you still need an address. This info is what they are using to identify your device.
Most traffic is already encrypted (httpS) so someone spying on you wouldn't know the content of your communication only who you contact. But without a VPN a man in the Middle could see who you are contacting. E.g. looking up pornhub. With the VPN it only shows you looking up the VPN.
From my understanding your statement seems correct, but it's also lacking a bit. Unless you also randomize your mac address (grapheneOS does this) they can still map your position and visiting times. Additionally not all of your phones data goes through the VPN, something like a phone call/SMS isn't encrypted unless you're using an app to make the call.
Yes, they are thinking of a VPN as a privacy tool, not strictly as a security tool as in your example. Privacy will be compromised.