Yes!! I thought the same thing! But I wasn't sure, because it was so long ago, almost 44 years.
My recollection is that it was shown from an angle that placed Ziegler between Nixon and the camera. Ziegler spun around, and his sport jacket flared out on one side. Nixon spun him so hard he slightly lost his balance, but recovered rapidly.
Also I think he was holding some papers in his right hand, which he almost dropped.
Exactly, that's the one I've seen! Probably CBS' footage, since that was my preferred network in those days... Oh, the shame!!!