Printing is immaterial to how the image is recorded.
That much is true.
What is "blur at the pixel level"? Blur can only be observed in images, not in pixels, and that requires some physical manifestation, print or display, and that menas it will have a physical size. That physical size is reached by magnifying the image captured by the sensor (whatever its resolution or the number of pixels present) by a factor that depends on the sensor size. Thus, images from smaller sensors will be magnified more, so any blur present will be more apparent.
Part of that makes some sense, I guess, but it would only apply if you routinely discarded the parts of your FF image that wouldn't fit on an APS-C sensor.
That's not how the real world works though. On different formats, different focal lengths are used to achieve comparable framing. Do that, and you need to magnify by different amounts to get to the final print/display size, and that's where subject blur is magnified.
If you don't do that, and just crop the larger image to match an APS-C frame, then the magnification and blur would be the same, as you say. That's the part that makes sense (in a limited way, given that you've paid the FF price, but are only ever using APS-C capabilities). However, since you would necessarily have to throw away the content that would have made the scenes different, that part doesn't follow.




