The men of the Lake were obviously very joyous that Thorin, the son of Thrain, who was the son of Thror, had returned. There was a great celebration and the men believed that gold would soon be flowing down the river, and pouring out in great amounts. If you were in the viewpoint of the men of the Lake, would you immediately accept that the city would soon be overflowing in gold or would you be hesitant and try to find out more information?
The men of the Lake were obviously very joyous that Thorin, the son of Thrain, who was the son of Thror, had returned. There was a great celebration and the men believed that gold would soon be flowing down the river, and pouring out in great amounts. If you were in the viewpoint of the men of the Lake, would you immediately accept that the city would soon be overflowing in gold or would you be hesitant and try to find out more information?
In my opinion I'm suprised that they believed him right away. I mean everyone else they have encountered have questioned about who they were and where they were going. Although most of the "things" the dwarves and Bilbo have come across have been bad, unlike the men of the Lake so that is probably why they didn't question them. So if I were the people, I would be questionable if Thorin was lying about being king and would probably think that gold wouldn't come down the river, because they still have to defeat Smaug and everyone else has been unsuccessful at killing him. But, since they believe him (that he is a powerful king like his dad and grand dad) then maybe they think that Thorin will be able to kill Smaug easily.