Is a weaker hand ever preferable to a stronger one (assymetric info)

[_D&L_]

An interesting assymetric information information problem appeared to me while working on my poker program:

Is it ever possible that you would prefer to be holding a weaker hand so that you can rule out possibilities that your opponent is on.

For instance, if you are holding a pair on showdown (so no draws left) and your opponent bids, would you rather have a better kicker, or maybe a lower kicker that eliminates a few potential straight combinations and maybe is of a different suit - so while not giving you a flush, reduces by 8 combinations the likelihood your opponent is holding a flush.

If your going to call no matter what, u want the better kicker, but if you are at the margin between calling or folding (or alternatively between calling and re-raising), the lower kicker may rule out more straight, flush, etc, combinations than a higher kicker would protect you from hands that would otherwise beat you.

Keep in mind my question isn't how likely you think this scenerio is, but is it possible? For programming purposes, I distain assumptions. So can anyone prove it would never happen? Keep in mind your opponent is not calling you with a random distribution...