Allowing Frodo to go when he was so close to Denethor's grasp will set up great conflict/tension between Gandalf/Faramir/Denethor in ROTK. So... like I said, much was going on in those scenes.
But that's my opinion... and that and a $1.32 will buy you a gallon of gas as we say in these here parts.
If memory serves....wasn't there a battle at Osgiliath (sp?) that happened before the Council of Elrond? Could PJ just have moved that encounter? I don't have my source material with me today!