Impossible to tell whether the GA was correct without knowing the carrier and the fare rules for OP's ticket.

While it is true that many tickets lose their value if you no show (which OP was effectively doing), others may be changeable, changeable on the day of (SDC) (with or without smallish fee), or changeable for a fee + fare difference. No way of knowing without knowing the rules for OP's ticket.

As to the specific issue, the FA was wrong and on most carriers has no authority to handle ticketing. The GA was largely correct if correct about the fare rules.

Not only unworkable to allow individuals to decide which rules they must obey, but it would become the immediate FT scam of the week (show up last to board with a bag and they will rebook you for free).