When the King inserts himself into Thai politics, he is perceived as acting altruistically, out of sheer necessity for the benefit of the people. This is, as others have mentioned, the result of decades of political maneuvering. The King Never Smiles, does a great job of outlining this strategy, but Duncan McCargo's article on "network monarchy" (http://www.polis.leeds.ac.uk/ass...) helps clarify how the King relies on extensive political networks to achieve political goals from behind the scenes, while still appearing "above" routine political haggling.
Another explanation for Thai admiration of the King, apart from strict lèse-majesté laws which forbid substantive criticism, is his status as a prominent Thai Buddhist theologian. The King is commonly believed to perfectly articulate fundamental Buddhist principles and when the King does appear in public, he frequently references Buddhist principles to support his vision of Thailand’s future. The King is therefore free to cloak political arguments within Buddhist rhetoric, adding another layer to the general mystique that his regime actively seeks to promote.