If you simply copy the file using the file system you won't get any degradation. As you suggest, in that case you are simply copying 1's and 0's.
The loss in quality comes when running the jpg compression algorithm which happens when saving from an image editor. This is because the jpg format throws out some image data each time it saves in order to compress the file and save space.
This can often cause some confusion about exactly when jpg images get damaged and what you should or shouldn't do with them to minimise this. If you open a jpg, edit it, save it, close it and repeat this cycle you will eventually introduce noticeable damage (how quickly depends on your compression settings).
However, you won't get an incremental loss of quality if you keep saving the same file during an editing session (as a precaution against the computer crashing for example) as long as you don't close and re-open the file each time. This is because whilst the jpg algorithm is applied to the new saved file, it isn't applied to the in-memory copy of the image and therefore no damage is caused to this. Effectively when you make your final save and close the file you will have applied only one round of the jpg algorithm to the final file on disk.