Why are coins left on headstones?

I'm not very sure the accuracy of this, but I've seen on television (History Channel? Discovery?) that ancient Greeks and later on Romans left a pile of coins over the tombstone of the departed loved ones. The coins were meant to pay Charonte (in the greek mythology it was the entity responsible for delivery the death over the Lethe River). The Lethe River was believed to erase all the memory of the deaths. Nowadays I've heard and seen some tombstones with coins engraved but don't know the true meaning.