Also noticing the part was spinning under driven power against the MDF wheel (at 8:00 into the video). If done by hand, the give of the MDF would've been less of an issue. At driven speeds, most any metal is going to make the MDF deform out of flat, as it's very soft against any driven tool.
By hand, MDF works well as a stropping substrate for flat-bevelled knife edges or tools like chisels, so long as the edge itself isn't allowed to dig into it under pressure and by which the MDF would be gouged or otherwise deformed. My favorite finisher for chisel edges is an MDF block with green compound applied (dry compound suspended in mineral oil and 'painted' onto the MDF).