Internally, the line-in is routed manually from top to bottom, usually with 2 green wires which surface in the battery compartment.
Several people have reported such a mis-wiring. Apparently the chinese manufacturing wasn't too reliable about this job.
The elegant solution indeed involves soldering, but the fact that it's wires makes it rather easy, no need to cut PCB traces or such. If you don't want to open the device, you may do the crossover in the battery compartment.
With software config of the MAS, we can swap left+right at the output, but not at the input, afaik.
Jörg