I would check CMP Kinase - does it have similar selectivity? Differences between C and U (especially with respect to hydrogen bonding of the base) are not necessarily all that minimal - most likely the enzyme employs a few strategically positioned residues to create hydrogen bonding networks that favor U over C. Which also means that the phosphate-cleaving residues have to swing into action when the correct base is recognized, meaning that I wouldn't be surprised at all if at least one of the catalytic residues is also shared with the substrate-specificity residue set.
Just a guess, of course. Too busy to look it up :)
Artem