How does the Savant interact with the Mystic Theurge?

A character in a game I am running wants to use the prestige class mystic theurge (Dungeon Master’s Guide) to advance the caster level of his savant.

The savant base class (Dragon Compendium) gains a kind of spellcasting progression starting at 5th level – the character gains arcane spells – and by level 10 acquires the ability to cast divine spells as well.

By 12th level, the savant would have access to 3rd level arcane spells and 2nd level divine spells.

At this level, the savant possesses the necessary skill ranks and the spellcasting requirements for the mystic theurge prestige class.

However, can a savant even benefit from the mystic theurge? The player of the savant claims that the mystic theurge progression will elevate his caster level; since savants have a caster level equal to one-half their savant level, a character who progresses savant 12/mystic theurge 8 will have a caster level of 14 (instead of the caster level 10 that a savant 20 would have).

… I am less sure that the mystic theurge interacts this way with the savant – indeed, I am unsure if the mystic theurge can even interact with the savant at all! The savant has no "spellcasting" class feature for the theurge to advance…

More controversially, the player also claims that the mystic theurge progression would double advance his savant spellcasting progression. Since the savant is both the arcane and divine spellcasting class, each level of mystic theurge would give him two levels of progression with his spellcasting in the savant class – which would rapidly run him out of spell progression, if the theurge can in fact do such.

My questions are:

  1. Can the savant base class benefit from the mystic theurge in any way? Either by increasing the caster level or advancing the spellcasting progression of the savant, or, in some other way the player or myself haven’t thought of?

  2. Does the savant truly qualify for the mystic theurge? While I am confident that the answer to this second question is probably a yes, I’d prefer it if there were a valid reason to disqualify the savant from the mystic theurge other than just GM fiat.