My use of similar features goes back 30+ years to the PLATO systems developed by the University of Illinois & Control Data. Appearing in the user list was an option that first had to be enabled by the administrator (group/course owner) creating the signon and then turned on when the user explicitly allowed himself to appear in the system-wide user list. Privacy was a paramount consideration in all aspects of the development of that system.
My preference then and now largely has been NOT to appear on- or off-line to anyone who doesn't really need to know. Even fewer people need to know when I was last active. On PLATO, for example, that information was available only to group administrators who created/deleted signons and to certain operations & systems personnel, whose access might often be logged.
Likewise on FT I'm basically always on but often working. Others have no need to be aware of my presence (mods & admins excepted).
I see the date & time of last activity as really two issues.
#1 is that it's none of anybody else's business (again, mods & admins excepted). I believe vBulletin allows the very fine-tuning of what is shown publicly in a profile. The date & time of one's last activity should be unflagged. There's a completely different interface where mods & admins can still view user information.
#2 is that I would view the failure to update the date & time of last activity for invisible users as a bug that should be fixed. It could be fixed via local mods, but since IB also now owns vBulletin, let them have at it through their own channels.