I think (and this seems too simple but, seems to work... hear me out) that what makes something "genuine" is it being true. So, take for example my genuine experience of my hands as I type. It's genuine, because it's true. If I were instead having phantom limb syndrome, well then that's not true, and we say it's not real experience. One is a genuine embodied experience because it aligns with physical reality. The other doesn't.

In this sense, machines have embodied experience when what they experience correlates well with the world. So there's not much to embodied experience at all really. As in humans, the ability to distinguish genuine embodied experience from illusion is important to achieve their goals. So too can machines benefit from this ability to sense and differentiate embodied experience from illusion.

Continuing on this tack -- my self-consciousness is self-consciousness only when it's true. If the thing doing the computation is not in my brain, but elsewhere, believing it's in my brain is not true. Similarly for machines. So Anderson's "intelligent disembodied mind", if it knows it's a computer, has genuine consciousness. If it believes it is a human somewhere running around, it is actually stupid in a very deep sense, and not self-aware in the slightest. Physical embodiments matter, and today's level of machine consciousness depends on it.