I don't think instantaneous forces are a factor here, those would be so brief they would be unmeasurable and definitely not something the bar is going to have any effect on. The bar is designed to respond to continuous loads not micro bumps.
Now that I've thought about it a little more the asymmetry has more to do with the length of the lever arm being different on each end. The length of the bar will act as a single spring, however because the length of the lever is different on each side the resulting multiplier will be slightly different. So although the spring tension is equal across the length, the lever length twisting the bar is different.
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