Regarding the ordering of your certs, whether I represent the sellers or buyers, I always call the Municipality where the property is located to check the zoning and fire status before submitting a contract or posting a listing to ensure there wont be any gliches. If there are any discrepancies they can be addressed before the contract is signed. This is a good safeguard that I always follow. In this way, the sellers know the cost, cert and time requirements.
Once the contract is signed, and the Home Inspection and termite are completed and any issues are resolved we then wait for the appraisal to come in for the value on contract. Once this is accomplished, the seller should order the CCO and Fire Inspections. As all the aforementioned is accomplished, I normally check that we are in compliance with the deadlines on the contract. If not, then an Amendment is drawn up to facilitate the necessary time needed.
Following these guidelines normally insures a better outcome for both the buyers and sellers.
That said, in reference to the particulars of your deal, if the home inspection report isn't back, I wouldn't have applied for the CO yet. So you're good. I think you're ahead of where you should be, and the buyers could have gone and done it themselves, no one would have stopped them. All they would need is entry to the property at the time the inspectors were showing up. I am sure you would not have denied this. So tell them to quit their belly aching.