That is the way it use to be around here,just changed it recently.
Must be a local code. IFGC vent tables will allow single wall galv. In fact, furnaces can also be single wall vented when the data meets the vent table requirements until it connects to b-vent prior to going through the ceiling.
Dormont, who invented the stainless flexible gas appliance connector rates their connectors at 5 psi but actually tests them to 125 psi. Gas only. They make special connectors for specialty gases. You can use those copper flex lines in seismic zones but not gas flex.
Regardling the galvanized vent connectors, can you say where this is code? It is allowed by both the IFGC and NFPA 54 except in concealed and unconditions spaces such as attics, crawl spaces and walls. Single walled pipe carries a 6inch clearance to combustibles. The sizing tables in the gas codes assume a 12" rise right off the draft hood before any offsets. You should never put an ell right on the draft hood or it may find it easier to spill into the CAZ rather than up the stack. Make sure you screw those pipes together--I rarely see screws or supports.
If your AHJ requires something that is over and above the gas codes, ask him where you can get a copy of the local ordinance. If there isn't one and he's just playing God, he cannot legally fail an inspection or hold up a permit.
I'm guessing a DIY'er who cannot sweat copper used those flex lines.