FYI, my divorce lawyers came up with a good approach that should address both sides of the concerns brought up here so now I'm just acting a devil's advocate for this current debate since I'm responsible for starting it.
I've been trying to analyze this specific clause for a while now. I agree with PayrolGuy that "denies" is a pretty critical key word. It's the end of the sentence that actually ends up needing some more breakdown for me. For the sake of argument, if it was my personal workstation, then by definition, it is NOT "available to any other user" and therefore this clause may not apply in that situation.
However, then to what time length does "available" extend to? If someone is eventually hired to take my place and is supposed to use my former workstation, then that computer then becomes "available" to that user, but certainly no longer to me. Can the law still apply that far down the road? We have to consider what's reasonable expectations for normal employer/employee separation of work relations.
Also, it is an awkward wording since I read it as they meant actively causing new problems as per their specific example of "access to the Internet" which would mean like I somehow after getting fired figured out how to remotely shut off her internet.
Anyway, like I said, this issue has now been handled in a wholly different way so this above is no longer a real-life situation, but it would still be nice to come to a consensus for future reference.
FYI, it also occurs to me just now that I definitely set up her workstation to access mine when I first set everything up so she DEFINITELY has the password saved on her own computer... LOL...