The mention of Thráin in The Hobbit only served one purpose: to establish how Gandalf acquired the map and the key. There was no thought-out backstory at that time. While some changes (such as how Bilbo acquired the Ring) were retconned in a later edition of The Hobbit, this detail was likely considered too inconsequential to include (even if Tolkien himself had noticed the discrepancy).
More information about how The Hobbit came to be part of the larger universe can be found in How much of the Middle Earth universe had Tolkien invented when he wrote The Hobbit?. In short, The Hobbit was unrelated until The Lord of the Rings was written, at which point both were posited as taking place in the same world as that described by (the yet unpublished) Silmarillion, but at a later time.
That said, there may be some mention of this in The History of The Hobbit, which I have not read since shortly after its publication in 2007. [Update: @ibid added a relevant passage to their answer.]
Also, there's simply no mention at all of Balin or Dwalin reacting to the story of Thraín in The Hobbit. We can simply assume that all the dwarves present are familiar with the story of Thraín setting out, and that any further exposition was possibly cut off by Thorin's curt dismissal of Gandalf's introduction.
[Gandalf speaking] "And Thrain [sic] your father went away on the twenty-first of April, a hundred years ago last Thursday, and has never been seen by you since--"
"True, true", said Thorin.
"Well, your father gave me this to give to you; [...]"
One can easily imagine Balin and Dwalin nodding along in agreement with the story they themselves were part of as Gandalf began it, until Gandalf skips to the end after some impatient prompting by Thorin.