HTTPS is not VPN tunnel. What are you talking about? A metaphor?
The rest sounds logical but it doesn't invalidate the possibility for using it as an anti-privacy feature.
Some searching lead me to https://tools.ietf.org/html/rfc5246#section-7.2.1 but from that explanation I don't understand at which point exactly the close_notify should be sent (after downloading the document or at any other point), what effect it may have if the client is not sending it etc. Seems quite a complex matter as a whole (at least for me) and unfortunately I don't have the time to dig deeper into it right now.
