Assuming that the problem is posed and understood as an artificial puzzle (rather than a real scenario with real people), what reason would there be to question how they know? Of course you're supposed to assume they know. It's a puzzle, and someone is telling you precisely what you're to assume.
On the contrary, there are many unspoken things one must assume to solve this puzzle "correctly"; that Albert and Bernard are rational, honest, cooperating, and have a certain penchant for communicating novel inferences they make instead of just blurting out "we don't know" out of boredom, laziness, or frustration.
Logic puzzles where one must assume so much are not about pure logic. They are "logic" puzzles. If you aren't made aware of the assumptions that were made in building the puzzle, the solution you arrive at may not match the "logical" one.
Is it really such a big leap to assume that fictional people in a logic puzzle or riddle are telling the truth? I don't think so. To me, it's very clear that the names of the people are chosen arbitrarily (with first letters corresponding to the first letters of the alphabet) and that the things they are saying are simply a way to convey the logical constraints to the reader. It's very obvious to me that the fictional people, their names, and the fact that they are speaking aren't actually relevant to the logic puzzle.
