The best, and clearest response I can think of is:
Your computer is legally your property. Unless a person has a warrant for the data on your computer, they cannot access it. They cannot control it. They have no easy legal way to get the data back and certainly wouldn't have access to who may have been a recipient of it through your willful or unwillful actions. Not without at least expending some major $$ on an attorney for warrants, subpoenas possibly court, litigation, prosecution. I think you can see where this is going.
All the above, which are great answers, aside; Why would a company want to give anyone their knowledge base, and potentially leave themselves open to litigation down the road?
The example of: You take your personal computer into work with you as you're working on a Saturday to get caught up. Let's say in between your work, you want to access your favorite remodeling show, and chat with your neighbor about the next home improvement project.
As innocent as this sounds, technically you're breaking corporate policy and could be fired for 'stealing' bandwidth or violating policy or any number of corporate policy's that fall under the "I have read this document and agree to its terms" which we never, or rarely read.
Technically, you are 'stealing' bandwidth. It is their network and you're accessing it without express permission on a day when you don't have express permission to even be on the premises. Or at least that could be their argument if things got sticky.