well not necessarily, my boss' EG is fitted with Integra's b18 and it doesn't need HOBC.
Check the owner's manual but my guess is that you should get HOBC mixture for this and 11-12 is pretty fine for this car. This is a simple VTEC engine, even the new i-VTEC would do 11-12 locally but again if you really are hypermiling then people have done 23 with their CL9's
Get HOBC from panj sarki, F6 Caltex or F7 Shell. Try it and share results, hopefully you would get 13-14 with it but if you don't, then don't be sad as your engine won't knock and would be smooth meaning longer engine life, so its a win win
Oh and I would say remove this blockage, get your car OBD2 scanned, it will show you if all sensors are working fine.
Does your car have a catalytic converter? I am not sure about this one.