I don't think a replay or infolog is needed here - the explanation is simple: in most missions each AI is only permitted to build a specific whitelist of units, which generally doesn't include the units of the factory the player starts with.
Things could probably be arranged so that the AI can build units from all factories but can only build specific factories for itself. It would require significant grunt work to fix all the missions though.
In a normal skirmish game the AI should use any factory it is given I expect.