Agreed, however, in order to have the same fov on 2 cameras with different sensor sizes, you must adjust the lens' focal length. This in effect changes the DOF
It is unhealty for a discussion to mix up different aspects. Stick to narrow subjects, abstracted from others; otherwise we end up with arguments like my eyes are not as good as yours, so the DoF for me is much larger than for you.
I am having a very hard time understanding how pixel size changes DOF at all
Well, then back to the basics.
What does it mean to be in focus? It means, that different light rays from a point of light meet at the focal plane (at the level of the film or sensor). Out of focus means, that the light rays meet before or (imaginarily) after the focal plane; anyway, they arrive at different points on the focal plane.
When these points are so close, that the difference is not perceivable, then we say they are within the circle of confusion.
Thie means with sensors, that as long as the light rays arrive within the "catchment area of the pixel site" (i.e. over the microlens of a single pixel), then one can not differentiate between in-focus and out-of-focus. However, if some of the light rays arrive at other pixels, then that point of light appears to be at several pixels at the same time.
So, the larger the pixel site, the larger difference is tolerable.