I'm not comfortable with the current etymology. First, I'm not sure it's an etymology — it's more a guess as to the metaphor behind the idiom, as opposed to the usual account of the changes in the forms and meanings of words. I'm not against explaining a metaphor, but I'm not sure that such an explanation should be listed as an etymology.
Second, I'm not convinced it's correct. Personally, my image of this idiom is of having to swallow (i.e., accept) something you'd rather not. You do it, but it leaves a bad taste in your mouth. Nausea is optional, and in any case is the effect, not the cause.
In the examples given: A subordinate reluctantly accepts orders; Someone accepts the news of having helped a killer; A basketball player accepts that, despite a terrific effort by a first-class team (speaking as a Tar Heels fan), his team didn't win. -dmh 14:38, 5 Apr 2005 (UTC)