The diode-ring mixer operates by switching the RF signal straight through to the IF port on one half-cycle of the local oscillator, then switching an inverted version of the RF signal through to the IF port on the next half-cycle. It doesn't depend on the non-linearity of the diodes for its operation - it treats them as switches. Best inter-modulation performance comes from keeping the diodes hard on or hard off, minimizing the time for which they are in an intermediate state.