Yes they do.
And my brother in law (and sister) who is presently doing work (at the branch in new york and now colombia)there has a wireless laptop.
Many puter savvy ones may have thier own firewalls preventing access or monitoring though if directly using the society's server they may be able to access some info.
The fact the bethelite was monitoring his dads pc is simple, he probably put on a remote monitoring keylogger on there. Some are undetectable but all you need is access to the computer to install and the other users may or may not know of it. The data is then emailed or can be seen online.
Hope that helps.
Btw I'm no longer a NOOOB
-Riot of the Junior Member Post Junkie Class