That would be "die Brüder sitzen um den Tisch herum", which could be the same as "am Tisch"/"at the table", but for all we know, they could be sitting on the same side of a rectangular or square table, in which case "around" wouldn't really be the best way to describe their seating arrangements. On the other hand, "sitting around the table" is definitely more common than "um den Tisch herum sitzen", which is rarely ever used because it's so clumsy, so maybe report it and see what the team makes of your answer.
I'm only a beginner, so I can't really address the idiom 'at table,' but I think the point of the lesson is for you to recognize that the contraction 'am' contains the article 'der.' Plus, 'at the table' could mean at any table doing anything, whereas 'at table' implies gathering at a table specifically for a meal. Hope there is someone out there who can answer your question more completely.