According to toller :

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.

Think of it this way: multi-wire branch circuits are primarily a labor-saving
technique when you need two circuits in the same place on the other side
of the house. The time saved can be quite significant in more sophisticated
wiring jobs.

It often doesn't save much money in materials, because due to the way
demand/supply/volume works out, two lengths of, say, 12/2 often cost
less than one length of 12/3, despite it needing two copper conductors
_more_.

If your electrician is on hourly rates, it's probably better to go with the
12/3 if circumstances permit.

The only real drawback is that people (and even some electricians!) aren't
very familiar with them. A secondary problem can be you might not be able
to figure out which circuit is overloading if the breaker trips. But
there are ways to diagnose that. Another issue is if the installer
is sloppy, lazy and/or doesn't know about the neutral pigtailing requirements.

I use them occasionally when it makes good sense.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.