I just assume that writers can conjure up factories by fiat if they wish. Of course, this hypothetical C doesn't have to be a Horse product, though they'd be the most natural source by inclination.
Nope, nope, nope... Once upon a time, in the Wild West of the early days of BattleTech, maybe.
These days there is actually a factory list, by Era, that is used for this work. If a factory is needed, it goes to the Line Developer or ALD for review.