Agreed, and I want to expand that a little:

Muggle science determined that muggle minds are contained in muggle brains, and Harry has been reluctant to let go of this idea even though there are observations against it and he has seen that magic can freely violate very solid muggle conclusions like conservation of matter.

Even if muggle brain damage seems to damage the mind, it could be that it damages the mind's interface to the body. Here in the real world, this dualism adds additional complications and doesn't help explain any evidence. In the HPMOR universe there is a great deal that would be explained by mind/body dualism.

Animagus transfigurations almost require it. Skeeter's mind is not contained in the physical arrangement of a beetle's brain. Therefore, her mind isn't just a physical brain in this world. Her brain could be held in some extradimensional pocket and interfacing to the beetle. Her mind could be running on a magical, rather than physical substrate (always or just during transformation?). She could have a soul. (And some versions of "mind on a magical substrate" would also qualify as "souls".)

As DanArmak says, Quirrel didn't just have backups of himself in Horcruxes, he was able to think and perceive while this was his only form of existence. Those copies were running, thinking, planning. They were also connected to each other, and still are. Quirrel was not revived from the Pioneer horcrux, but he has the memories of the Pioneer horcruxes experiences. The pioneer plaque or a pebble or whatever is not a physical substrate that a mind can run on by any natural-to-muggle-science means. Again we have dualism. Brain in another dimension, magical substrate, soul. And brain in another dimension gets pretty strained here, I think.

You, boy, you brought that about, you freed my spirit to fly where it pleases and seduce the most opportune victim, by being too casual with your secrets.

Here Quirrel's mind is totally disembodied through the help of the Resurrection Stone.

Ch. 1:

There's a quote there about how philosophers say a great deal about what science absolutely requires, and it is all wrong, because the only rule in science is that the final arbiter is observation - that you just have to look at the world and report what you see.

I observe a world where minds are not just physical arrangements of brains. The "we are just our brains" hypothesis is being falsified all over the place in HPMOR.

For me there is no question about whether disembodied minds exist in this universe. My questions are whether minds are disembodied all the time or just when magic requires it. Whether muggles also have disembodied minds that are just much more inaccessible to observation. "Minds are always disembodied" seems more elegant by far than magic translating your physical brain into another equivalent form and creating an interface between that and your body only during animagus transformations and other such events, translating that back when returning to human form, and your mind just being a brain at all other times. That would be way more complicated than dualism.