Check out rule 4 here
Gehrigs rules on river play
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Since nothing that beats us will fold, it must be for value.
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Pardon me, but... Well duh!!
The important thing about river play is not whether you are ahead or behind but how you maximize your payoff in each situation. In this case I will claim that both c/c and b/f are likely to cost you 1 BB when you are behind. So the important thing is what maximizes your payoff when you are ahead. In this case I will claim that villains are much much more likely to call 1 bet with a worse hand than they are to bet it for you. So bet is better when ahead and when behind c/c and bet are equally bad. All in all bet beats c/c.
To convince me that c/c is better than b/f you have to convince me that a) villains are more likely to bet with a worse hand than call. And b) It is likely that one of the villains will bluff raise you of your best hand. If you can convince me of this I will give in.
The stuff about "if you want to invest 1 bet then c/c" has nothing to do with maximizing your payoff. You want to choose the strategy that responds best to your opponenents likely choice of strategy for their likely hands.
The next question is then how to respond to a raise. Usually in multiway pots river raises means villain has the goods and a fold is in order.