No, that's obviously not true. For example. A bad value trade is offered. Team A doesn't do it because it's bad value, team B doesn't do it because despite "winning" the value of the trade it hurts their team, it's not a need. Both teams hate it, but the value sucks.
If I'm in Spain and want to take a train somewhere, there's nowhere around that I can exchange American Dollars for Euros, the train ride costs 30 Euro, I have 30 Euro and there's an American next to me with 80 American Dollars who would like to ride the train but it isn't absolutely necessary. The Spanish dude next to us suggests he give me his 80 Dollars for my 30 Euros so he can ride the train. The value of his suggestion sucks because his 80 Dollars are worth more than my 30 Euros, and the guy doesn't want to pay that much to ride the train, but I need my 30 Euros to take the same train ride, so I also say no. Both sides say no to the Spanish guys suggestion and the value also sucks