Perhaps, but the two breakers can be decoupled (separated electrically)
easily by taking off the plastic connector that ties them together.

Some are coupled internally, though you are probably right.

Does my suggestion that it's 12/3 from the breaker box to a j-box, then
from there using 12/2 make any sense? It seems like a lot of trouble to
save a little on wiring. I can look into the breaker box next time. The
house is oldish, but was remodeled within the last 20 years I'd think.

Again I apolgize for reading your post too quickly; I thought you said it
was 12/2. I have to stop reading these things when I can't sleep.
Yes, you only carry 12/3 to where the two circuits split, then it is 12/2.
There are two hots and a neutral to the first box, and then the neutral
branches and the hots go their separate ways.
It saves a little wire, is less to stuff through little holes in the joints,
and gives less voltage drop. If the two circuits are reasonably balanced,
then nothing comes back over the neutral, so the resistance is lower for a
one way trip.