Probably then he's got the tech skills to back up giving you free reign, or maybe he trusts you and understands that you can do whatever you like on your own computer. Any maybe the assistant doesn't have those skills/understanding/trust and it's just easier for him to tell her "no non-school related internet activity and here's how to ban someone for the day".
Is there any way you can check who's on before accessing the net? Or is the only way to find out to risk a ban?
Alternatively perhaps you could ask him to make you an exception when she's covering for him; if you have a good relationship with him then this may be a viable solution. Especially if you offer to help him out, maybe by offering to put a pile of returned books back on their respective shelves when you're in. And doing the same when she's in may also score you some points with her, if she can see you're helpful and trustworthy then she may give you a bit more leeway when she sees you on her monitor again. Don't view her as an "evil chick" but as someone trying to do her job as best she can.