Island sink plumbing code

Finally our renovation started. I wanted the kitchen sink to be on the peninsula, with countertop space on both sides, and its right edge would be 2 feet from a full-height cabinet. The plumber is tell me that the vent pipe of the sink has to be 6" taller than the sink, and no more than 1 feet away. So he suggested that I either have the peninsula be split-level, with the bar area 6" higher than the counter, or move the sink next to the full-height cabinet. Otherwise he says we may not pass DOB inspection. Is this true? I see so many island sinks that are quite far away from anything taller than them. Are they all done illegally according to nyc code?