Don't you find it rather odd that the sun and moon could come within a few kilometers of each other and yet seem to have no gravitational influence on each other's orbit? It's a wonder that they don't actually crash into each other.
They do gravitate towards each other, but they aren't close to each other for long enough to collide.
Check me if I'm wrong, but the moon isn't moving very much faster than the sun, is it? As you said, the moon approaches to within a few kilometers of the sun. Gravitation is believed to travel at or near c. How is it possible for those two bodies not to be close enough for long enough to attract each other enough to cause a collision? At the very least, the massive gravitational influence of the moon (on the order of a neutron star, if I'm not mistaken) should significantly affect the orbit of the far less massive sun, should it not? That is unless the sun and moon can produce gravitation, but are immune to it's effects (which would be a serious load of crap, even for you).