I might say "rush me to the local hospital" if I wanted to indicate a specific place, but being "in hospital" is a general condition entirely separate from which particular hospital you are in.
And thus one might use the general English construction, "being in a hospital" or otherwise the generic "a" instead of the specific "the" (though in the case of American usage, "the hospital" is generally taken to mean any hospital already). It does compare favorably to "being in bed" and "going to bed" just as in "going to jail" but it seems pernicious as a general trend. In a newspaper article I read recently, "the" was dropped in two cases, one of which was in reference to the city government. In Canada they don't use "the" in reference to Hospital or University, but on the other hand they do use it for freeway titles ("Take the 401 to Toronto" vs. our more common "Take I-75 to Toledo"). "I was up at University today." does seem weird when living in a town with two universities, I must say.
Bill was arguing that in the cases where dropping the "the" feels natural, there is also some implication of a verb within the noun. When you go to jail, you are also being jailed. We would say "we were going to the jail" if we were talking about a vist for some purpose other than to be incarcerated. Similarly "go to bed" means bedding down and (usually) going to sleep. There is an assumed verb that follows with the place. When a parent tells a child to go to bed, they don't mean "go upstairs and bounce on your bed while playing loud music or, usually, even "go read late into the night." They mean go to bed to sleep.
Go to market is another example. A market is a fairly simple place and you either go there to buy or sell things, one of which is implied in "we're going to market" (taking something to market leads to marketing it) - "we're going to school" also suggests that on arrival the speaker will be subject to some schooling. A parent would say "I went to the school today" when talking about another type of visit. It's an interesting theory, I think. And in this interpretation "I'm going to University today" might then make sense if the speaker is a student and University is considered synonymous with school.
As for a Hospital, well, it's complex, and there isn't anything you do at the hospital that uses some form of the word hospital as a verb, unless you stay there. Being hospitalized is a term we tend to reserve for an extended stay, and that's not what you meant.