We passed in a large Bay Area city by showing them the documentation for our dishwasher (a Miele) that noted that there was a built-in air gap and none was needed for installation. (Basically, arguing that the manufacturer's instructions should supersede code.) This was many years ago, though, and not sure if it would fly today. At the time I found and printed something from Los Angeles that they allowed this with certain brands of dishwasher--no idea if they still do--and also that a notoriously fastidious inspector in the little city adjacent to ours allowed it, though I don't think they looked at any of that in the end. I will say that we were cautioned throughout the project that it would just depend on who showed up to do the final inspection, but happily the inspector who had been out for most of the rough inspections did the final as well. We also have a wall-mount faucet and no other cuts in the counter, so I was dreading the final inspection!

Here's my very old thread on this from back when we were renovating--there may well be some more recent advice here too: https://www.houzz.com/discussions/2406462/air-gaps-and-california-code [side note...depressing to hear that the code has still not changed!]