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Both a Doppler shift and a Hubble redshift have kinematic origins, by definition. Both are caused by the movement of something...individual galaxies under gravity in the case of a Doppler shift. The other caused by expanding spacetime, which is also movement, but not of the galaxies themselves. Just like raisins in a dough, they may jostle about a bit when cooked (gravity/Doppler shift), but the dough rises and expands, carrying the raisins along with it (expansion/Hubble redshift). It's easy enough to see where they're coming from, but it's still a question of semantics. Unless, of course, they actually think that the redshift is being caused by actual movement of the galaxies through space (not with space, as is the case for expansion). That's a different matter entirely.
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