Assuming you didn�t lie on your CV, they already know your qualification level and have still decided to interview you, so you may be worrying unnecessarily. My advice is not to be drawn into the reasons. Just stick to the headlines of what you got and turn every question into an opportunity to highlight the good things you have achieved in the workplace.
For example, if they say �why did you choose that mediocre university� say �I was really lucky to be able to go to university at all and I thoroughly enjoyed the experience. It really helped me prepare for the hard work I had to put in later in order to achieve tough deadlines on the (so and so) project�.
Without wanting to offend you, you already sound a bit defensive about where you came from. If this company is �stuffy� that attitude will only make them feel uncomfortable. Also, you chose to apply to this company, so it�s time to move on.
Hope this helps. Good luck.