You don't want it exposed to the elements, the bones are frequently in pieces the size of a penny, and are remarkably fragile. It only follows that they would want to do the really fine work back in the lab.
Wrapping in plaster as they remove it from the surrounding rock makes the most sense. Come on up to the Museum of the Rockies, and you can watch the cleanup process and see the output.
We've all been told that fossils are dated by the layer of rock that they are in, and the layer of rock is dated by the fossils that they contain. I've always found that hard to believe. Especially in the case of Hell Creek, where supposedly an entire large area of 65+million year old rock has just been sitting in the open sun light for the last several thousand years. Interesting at least. Perhaps I need to make a trip there and see for myself.
We've all been told that fossils are dated by the layer of rock that they are in, and the layer of rock is dated by the fossils that they contain. I've always found that hard to believe.
AIUI prehistoric dates are corroborated by radioisotopic dating, similarly to using C14 for much more recent dates.
It's not on every story I read, so there could be something about the types of stories you favor that draws out the dismissers? I wonder how many clusters of users could be found based on which articles they like to click and comment on.