Listen to this recording:

https://www.youtube.com/watch?v=SgPuyzogFuI

It's from a Delta flight a few years ago that slid off the runway at LaGuardia in snow. The action starts about 5 minutes into that recording; Tower has just set up another incoming Delta flight to land, and is trying to confirm Delta 1086 has cleared the runway. Delta 1086 is poking its nose out over the water at this point, and the controller can't see it.

At around 5:56 a ground vehicle calls in to ask permission to cross the runway and gets it. Then the ground vehicle sees what's happened (Delta 1086 slid off the end of the runway), and this is where it gets interesting, because you see very quickly two important things:

1. Trusting the report: the guy up in the tower does not have a perfect view, and in fact in this incident he can't see what has happened to this Delta plane. He's getting an unsolicited report from a ground vehicle, but he believes it and acts immediately on it. If the report's mistaken, worst outcome is some planes circle a bit more before they finally land. If the report's right, though, the worst outcome is planes trying to land on a crash site.

2. Division of responsibility. From the moment the crash becomes known, it's the job of the emergency/rescue teams to figure out what's happened and deal with it. The guy in the tower probably desperately wants to know more about what's going on, but he's got planes stacked up waiting to land, and his curiosity is going to have to wait. Beyond getting confirmation of a couple unusual orders, Tower just lets the folks on the ground do their job, and sticks to doing his.

Here's a rough annotated transcript (timestamps are from the video), since I know people complain that ATC recordings are hard to make out:

6:08: Delta 1086, Tower? (trying to contact the plane that's just gone off the end of the runway -- Tower still doesn't know what's happened)

Tower, call 100, Runway 13 is closed. (ground vehicle has seen the accident)

Tower, red team to go onto 13.

Tower, you copy? Call 100, Runway 13 is closed.

Call 100, you said Runway 13 is closed? (Tower confirms what he's just heard)

Affirmative, 13 is closed.

Team red, Tower?

Tower, you have an aircraft off the runway.

6:45: Delta 1999, go around!

1999, going around.

6:50: The airport is closed. The airport is closed. We've got a 34. (ground crew saying this is bad enough the airport needs to close)

Call 100, say again?

6:59: Tower, you have an aircraft off 31 on the north vehicle service road, please advise crash rescue, LaGuardia Airport is closed at this time.

7:12: Good afternoon, Tower, Delta 2522's on the ILS for 13 (another Delta flight is lining up to land on the runway where the crash happened* -- they can't hear what's happening below)

Delta 2522, LaGuardia Tower, go around!

Go around, Delta 2522. (pilot confirms that he's going around)

From there on out, it's just Tower giving instructions to other planes on what to do, and a report from the ground to tell the pilot of the crashed plane (if he does get on the radio again) that the plane is leaking fuel from a ruptured wing.

Now: what if the ground vehicle hadn't gone out there? Or hadn't seen the crash in time, or hadn't been able to get a report to the tower in time, or the tower had hesitated a bit more in accepting the report and starting to reroute planes? A similar problem to the SFO incident, only instead of an occupied taxiway it would've been an occupied runway (and one that had already caused one plane to slide off in the snow, and now had emergency vehicles converging on it).

The point is, though, that this isn't necessarily a miracle or a lucky escape -- everybody is involved in ensuring safety, and that's what happened in both cases, providing extra layers of watchfulness which averted much more serious trouble.

* The runway is referred to as both "13" and "31" at different points; runways are numbered according to compass heading, so "13" means it's aligned to a heading of 130 degrees. The dual numbers are because you can take off or land from either end; the other number is always +/- 18, since it's 180 degrees around from the first one. In this case, the designation of the runway is 13 from one end, and 31 (for 310 degrees, 130 + 180) from the other end.