To my knowledge, recent naturally aspirated Hondas (last 20 years or so) do not go rich. However, their compression is high enough that, in order to not have detonation issues, they retard ignition timing significantly at high load. Running rich is an alternate tactic which allows a few degrees of ignition timing to be kept, increasing the energy extracted from combustion at high load.
High compression is double-edged. It provides really huge gains in efficiency at part throttle on any fuel, but can actually decrease power and efficiency at higher loads. Toyota's hybrid Miller cycle engines are basically a tactic to never let their engines run at more than ~70% load, thus allowing sky-high compression while never going into zones where they would need to pull ignition timing or run a rich fuel mixture.
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