Incorrect. "Invisible" is a privacy control, not just a UI filter. While the official client freezes the text, the backend still broadcasts live last_logon and last_logoff Unix timestamps in the ClientPersonaState packet. This leaks exact real-time sleep/wake cycles via the socket, completely bypassing the privacy toggle.
On the profile of a friend you can see the last time they signed-in to their account:
https://preview.redd.it/can-anyone-beat-my-last-online-frien...
Before it was public, and now restricted (for a couple of years already) to friends only.
I guess this is why they won't change it, since it's a feature.