I am sorry for the confusion, Rachel.
No the city can not overide the countys licensing requirements. My point being that the city inspectors are not going to ask for his license when they come out to inspect the job.
If pulling the permits requires that the person submitting them be licensed then the correct license will be required. They will not let a class G licensee pull permits for anything out of their class. They can hire a sub contractor to pull the permits and do the work. That is between the (general) contractor and the customer, howevewr if the sub pulls the permits then he isnt really a sub contractor as he becomes the contractor of record for that (part of) the job.
For this person to hire sub contractors he must have a general contractors license so that shoots that out of the water so to speak. The customer can hire a sub but they wouldnt be a sub in that case. Are you completely confused yet?
Basically the class G license allows you to do glaziers work and nothing more. Wood, metal, and glass doors fall under the general, doors, and rough framing class here in California, but we are wierd anyways.
Yes, Rachel you are correct. Glass only, no wood, or steel.
Personal opinion here ... If the work is done right, who cares!