People may not want (or have the authority) to change the deal, but if they are offended by you asking you do not want to work with them. It implies they are looking for a drone, not a real human being.
I've worked in several local government jobs in the UK, where budget (and 'Single Status payscale') constraints mean that the hiring manager normally doesn't have the authority to change the salary offered. Just asking the question has still given me an invaluable insight into the manager's way of thinking.
Unless you really, really want to work at $BIG_COMPANY, and you could only get an internship with them, or you are only looking for something for 3ish months. If you are looking for 'experience' and you have a year, get a paying job.