Yes, it is not random at all. You rank your firm choices. You will likely get your top 30 or so bids. I have never heard of a school which assigns your interviews "randomly." That doesn't make any sense. Anyway, in a lottery system, you must be strategic, because you don't want to use all your top bids on firms you likely will not receive callbacks from. Anyway, this is how Northwestern does it, as well as most of the top schools. It is also how Georgetown does it.
UVA is clearly different.
Pre-screening is dumb, because it cuts off the bottom pile of students. It frankly makes it harder for them to get jobs. They get less interviews.