This is the Foundation classic.
In a comparative article The Art of Saying Nothing the author recounts Asimov's Foundation exactly as described:
In the Isaac Asimov sci-fi classic Foundation, an envoy from the Empire arrives for 5 days of talks to promise a small planet Imperial protection against attack. Scientists at the Foundation then use symbolic logic to analyze the Imperial envoy's transcript, and reach this conclusion -- real guarantees of protection: zero; content of 5 days of talk: zero.
The interaction you recall is included below:
“But then,” interposed Sutt, “how would Mayor Hardin account for Lord Dorwin's assurances of Empire support? They seemed” he shrugged “Well, they seemed satisfactory.”
Hardin threw himself back in the chair. “You know, that's the most interesting part of the whole business. I admit that I thought his Lordship a most consummate donkey when I first met him – but it turned out that he is an accomplished diplomat and a most clever man. I took the liberty of recording all his statements.”
There was a flurry, and Pirenne opened his mouth in horror.
“What of it?” demanded Hardin. “I realize it was a gross breach of hospitality and a thing no so-called gentleman would ever do. Also that if his Lordship had caught on things might have been unpleasant; but he didn't and I have the record and that's that. I took that record, had it copied out, and sent that to Houk for analysis, also.”
Lundin Crast asked, “And where is the analysis?”
“That,” replied Hardin, “is the interesting thing. The analysis was the most difficult of the three by all odds. When Houk, after two days of steady work, succeeded in eliminating meaningless statements, vague gibberish, useless qualifications—in short all the goo and dribble—he found he had nothing left. Everything canceled out. Lord Dorwin, gentlemen, in five days of discussion didn't say one damned thing, and said it so that you never noticed. There are the assurances you had from your precious Empire.”