The Caloris Basin is a huge crater, but an impact capable of forming a large moon would have completely melted Mercury's crust.. However, an impact may have blown away much of the planet's outer layers, causing it to have an extremely large iron core. However, because Mercury is in a spin-orbit resonance, and thus has an extremely slow rotation, any satellite's orbit would tidally decay until it collided with its parent.
They say the Moon-making impact melted Earth, too. I have no trouble believing that, so I don't have a problem with it happening to Mercury. In fact, I think the melting is necessary in the moon-forming process via impact.
But you're quite right--Mercury is a real mystery. It does seem reasonable to assume that something big whacked it long, long ago, blasting off the outer layers entirely and leaving its oversized iron core. I'm pretty sure this would have melted everything, so Caloris happened much later, after Mercury had refrozen. But what happened to all that outer material? If it fell back to Mercury, then it would be there today and Mercury wouldn't be a nearly naked iron core, so it must have gone towards the Sun and either been eaten or tossed out of the solar system.
But that still leaves me with a question. On the face of it (without knowing how to do the math), I'd expect that to boost all that stuff to Mercury's escape velocity would have required a very high-velocity impact. Where did all that relative speed come from? You'd think anything more or less sharing Mercury's orbit would have had pretty much the same vector (thanks to Kepler) so the impact would have been fairly low-speed (which is a worry I have with the Moon-creating crash on Earth). I don't see much chance of a head-on collision due to (presumably) everything in the protostellar disk spinning the same way. So that leaves a collision with a highly eccentric crossing object, the odds of which seem pretty remote.
And what about Venus and Mars? For Venus, we can only speculate because of its fairly recent total surface repaving. But with Mars, we can still see the utterly huge crater covering the northern hemisphere. So where'd all that debris go?
In general, I'd say that the parameters are fairly tight. Note that the statistic says: 1 in 10 rocky planets around sunlike stars may have moons like Earth's. Since we only have four terrestrial planets, the chance of at least one having a large moon is about 1 in 3. The chance of at least two having large moons, however, is more like 1 in 37.
1 in 10 seems pretty high to me. But it's just a gut feeling.