All education loans have to be approved by the school*, which means that the school gets the final say on the total amount which you borrow. You can go under budget, of course, but you can't borrow more than that total. Any aid you receive is deducted from the budget too.
I find financial aid to be infuriating and paternalistic in general, but Dean Gottschalk is pretty great about working with you a) if you have good reason to increase your budget up front, or b) if something comes up and you need more money in a pinch. Plus, the school provides emergency short-term loans of up to $1000 with no questions asked.
And it's true that the computer loan can't go through Grad Plus - not a Michigan rule, as far as I understand. I didn't do a computer loan, so I'm not much help. They mean it, though, about only offering that your first year.
* I'm sure that some banks or other lenders offer something called an "education loan" that doesn't have to go through the school, but it would probably be a typical private loan that you would need to start making payments on immediately. I'm talking about the classic student loan in any of its many forms.