This is the crux of the confusion/misunderstanding which causes so much discussion on this topic. Many people don't understand the concept of "all things being equal" or the need to compare things at the same FOV and output size.I like the quote in big bold letters around 10:15. "All other factors equal - the smaller sensor will have the shallower depth of field."
Good video, worth watching from the beginning. He goes on to explain equivalency and crop factor and why once adjusted by physically moving farther away to fill the sensor with the same size subject the dof increases (because of being farther away). However we have been talking about staying in the same place and by cropping effectively reducing the size of the sensor. At least that's how I see it.
Edited: forgot to mention output in original post.
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