It's not as if Picard really needed Offenhouse's input.
Chiefly, the scene serves to show how Picard realizes the man isn't as useless and out of place in the 24th century as it first appeared... Why, he could make for a fine starship captain one day, coming up with tactical conclusions just like Picard's own!
As for the idea of the Romulans choosing to cooperate with Starfleet, and then turning a cold shoulder not twenty seconds into the dialogue... I don't think this really happens. What Tebok says is that cooperation will take place once either side figures out what has been going on at the Neutral Zone. At the time of the adventure, neither side has a clue, so there is no point in cooperating. Thus, Tebok's "Only if it's convenient and appropriate at the time": the time is not