The premise is that the dog can tell the aliens more about the real nature of human beings. I've been looking for the story for weeks now.
It's hard to be sure from that terse description, but you might be thinking of "Propagandist", a short story by Murray Leinster which was also the answer to this old question. It was first published in Astounding Science Fiction, August 1947, available at the Internet Archive; you might have read it in one of these compilations.
In the story humans and an alien race, the Masans, are suspicious of each other, while a third, implacably hostile, alien race lurks in the background. The Masans capture a dog named Buck and learn about humans from him. After the friendly meeting of humans and Masans:
The Masan scientist explained to Holden:
"It has worked out very well. With your atomic power, you can put any amount of energy into the power beam we've showed you, for battle with our common enemy. It is odd that we made power beams to fuel our interplanetary ships because we didn't have atomic energy, and you made atomic energy because you didn't have power beams!"
"There'll be a lot of stuff that will fit together like that," said Holden. "Our civilization will mesh nicely, as long as we trust each other."
"Yes," said the Masan, somewhat ruefully. "We intended to blast you to atoms, because we were afraid, and you intended to destroy our planets, because you were, also. I think both our races owe much to Buck."
"I still," said Holden uncomfortably, "can't see how you were able to trust us so completely. I don't think we'd have trusted strangers as you do us. Just because of Buck—"
"But it is because of Buck," said the Masan wisely. "We could extract all of his memories. All of them. His kind adores men. He would accept any cruelty from you. But you are not cruel. He would give his life gladly, but no man would ask it. He is yours, unreservedly, but you do not accept from him without giving in return. Do you know when the policy of the Planetary Council, to trust men without limit, was finally decided?"
Why . . . no," said Holden.
"When you entered the airlock of our ship," said the Masan, smiling, "and Buck met you. He had told us every secret he could impart. He had been almost a traitor, without knowing it. He had told us everything he knew of men. But when you entered our ship he leaped joyfully at you and you rolled on the floor together—you hugged him! You did not think of possible harm he had done. You were as glad to see him as he was to see you. That was when our policy was decided. Then we knew that men will always repay trust with loyalty." Then the Masan added, "That is, most men."