...if your destination is a big airport that suddenly shuts down for some reason while you are already circling over it, and the alternate is a smaller airport that cannot handle such traffic, exactly where are the guys short on fuel supposed to park their bus?
This kind of thing does happen occasionally, say with a rapid onset of un-forecast fog/thunderstorms, security incident, blocked runway, etc. The information propagates quite rapidly across the ATC network, so those who have still got some distance to run to the (now closed) airport can make alternative plans. Doesn't much help those who are now committed to destination and/or alternate, though.
When airports say they are full, it normally means that all the stands are occupied, so there are still taxiways and even the runway(s) left to put aeroplanes. You'd probably have to declare an emergency but that's better than running out of fuel mid-air. If the problem is an aircraft stuck on the runway, then you could land on what's left, performance permitting, or even on a taxiway. If it's a security issue, then you could land anyway and deal with it afterwards. If visibility is the problem and a precision approach is available (ILS/MLS) then, again, you'd just do it; if there are non-precision approaches only, or none at all, most modern aircraft will get somewhere close to the centreline and touchdown zone using GPS. There may be smaller airports within range that are not approved for your aircraft type and have no facilities but nonetheless provide a length of tarmac which is adequate to stop on. A controlled off-airport landing/ditching is preferable to an uncontrolled crash, in extremis.
Commercial aviation is overflowing with laws, rules and procedures. We do our best to observe and follow them but sometimes you just have to concentrate on getting the aircraft safely on the ground and sod everything else. Most pilots that I know have a series of fallback options for when things really start going wrong: plans A..D are within the rules, plans E..J aren't and from plan K you're just hoping you can walk away from it.
Fuel decisions and, really, most of aviation are based on statistical likelihood. This is a combination of regulation, experience and commerce. There is no 100% assurance of a safe flight, no matter how much fuel you take or how well maintained the aircraft is but if you keep "an eye to windward" and are prepared to fall back (gracefully at first) as far as is needed down the list of possibilities, then things will probably turn out OK.