I agree, but it isn't the act of weighing; it is the choice of an objectively better outcome that makes the choice rational. A rational person seeks to maximize an objective value, like, say, utility. So they'll typically assume that given a set of fixed alternatives with known probabilities of outcomes, a person will behave in the manner that will result in highest utility.
Choosing suboptimal outcomes is simply irrational. That's all there is to it.
My statement would assume that people would value money more than the thrill of playing. I think this is a safe assumption because most people eventually take the banker's offer, which seems to demonstrate that the thrill of playing does not outweigh the utility of the money in the briefcase.
I think the "Deal or No Deal" situation is more an example of emotional bias that leads to suboptimal results.