Yeah i was doing the exact same thing a few weeks back. and I have some theories! The forest is definitely a part of Hyrule (note the flying lights that are found only in Kokiri and The Lost Woods) Link travels with Epona in search of Navi and becomes lost somewhere near the dimension Termina. Then comes the encouter with Skull Kid and it is now my belief that the Keaton knew something of what was going to happen since he/she is so knowledgeable about the land and had bushes near the encounter. As you chase Skull Kid the bushes are a kind of marker, leading link toward Termina and the trials he will face there.
In a few Zelda games Link is led to a place or sent there by forces he doesn't understand (LA, OoX, MM, PH and maybe a few others) this is a common theme for starting a Zelda game, but the fact that not only Skull Kid but also the Keaton was trying to lead Link to his new adventure, plus the search for Navi sets up a very nice intro for the second 3D Zelda game. you may disagree with me but the Keaton does not show himself to Link right away but seems to be in the three locations mentioned by you Leix.
I just think that this THEORY adds a certain story element to MM that I like, a lot of Zelda is interpretation with all it's mute cut scenes and such.
So after some study I have come to the conclusion that Keaton knew of Link before he had arrived in Termina but chose not to reveal himself right away.