In article , NY
wrote:

This means that if you take a
photo on 120 film and on 35 mm, with appropriate focal lengths of the two
lenses to give the same field of view of the subject in both cases, and
use
the same aperture, the DOF will be less on the 120 photo than the 35 mm
photo.

nope. it will be identical for the same image quality.

So as long as film grain isn't the limiting issue, you should be able to
take a photo on 120 film with a lens that gives a certain field of view, and
then on 35 mm with a different lens that gives the same field of view, and
if you use the same aperture on both lenses, you shouldn't see a shallower
DOF on a print from the larger format negative?

if you do that, then the image quality will be different, which means
other characteristics may also be different.

also, depth of field is a function of the physical aperture (not
f/stop), so if you use the same f/stop on both (for exposure purposes)
you're actually using a larger aperture on the longer focal length
lens, thus the difference you're seeing (along with the difference in
image quality from the larger format, which can't be ignored).

That goes against everything I've ever learned about photography,

it's a common myth.

and the
fringe benefit of using larger film (the main one being finer level of
detail for the same type of film).

in other words, different image quality.

this explains it exceptionally well:
http://www.clarkvision.com/articles/dof_myth/
A commonly cited advantage of smaller digital cameras is their
greater depth-of-field. This is incorrect.

€ The myth, simply stated, is: smaller digital cameras have a larger
depth-of-field than larger digital cameras.

The simple reason why the myth is incorrect is that depth of field is
set by aperture, focal length, and a criterion for spatial
resolution, and if one keeps aperture of the larger camera the same
as that in the smaller camera, the two cameras record the same image
with the same signal-to-noise ratio and the same depth of field with
the same exposure time. Below are details explaining why this is
true, and Figure 1 gives an example.
....
Given the identical photon noise, exposure time, enlargement size,
and number of pixels giving the same spatial resolution (i.e. the
same total image quality), digital cameras with different sized
sensors will produce images with identical depths-of-field. (This
assumes similar relative performance in the camera's electronics,
blur filters, and lenses.) The larger format camera will use a higher
f/ratio and an ISO equal to the ratio of the sensor sizes to achieve
that equality. If the scene is static enough that a longer exposure
time can be used, then the larger format camera will produce the same
depth-of-field images as the smaller format camera, but will collect
more photons and produce higher signal-to-noise images. Another way
to look at the problem, is the larger format camera could use an even
smaller aperture and a longer exposure to achieve a similar
signal-to-noise ratio image with greater depth of field than a
smaller format camera. Thus, the larger format camera has the
advantage for producing equal or better images with equal or better
depth-of-field as smaller format cameras.