The oven box, where the food is cooking, is a separate chamber from the combustion chamber, and the water vaper that comes from natural gas combustion goes up the flue or out the top vent of the oven, not mixing with or effecting the contents of the oven box. The flames from the gas burner heats the oven box, and it's the heat of the oven box walls that is transferred to the food that's being cooked.
If the fumes from the gas combustion chamber were to leak into the oven box, your oven would be faulty and you might notice the taste of natural gas in whatever you cooked in the oven.
Broilers are different, and utilize the direct radiant heat from below the burner.