I flew YYZ-YUL-FRA with AC on a paid ticket and then FRA-DXB with LH on a reward ticket. The AC counter wouldn't put my bags through to DXB stating there were two separate tickets. Ok, fair enough.

However, on the way back from DXB, the LH agent put them through no problem.

Should AC have done this for me? I'd like to know for future flights.