Eileen,
Maddening isn't it! The buisness office at your hospital is not unique (hence why I don't worry about running out of work - unfortunately or fotunately depending on your angle). Sounds like your provider in the first secenario just cost themselves a bunch of money. In the second scenario however they could argue that you a responsbiel...right or wrong...they may try. I would call them and suggest they just go ahead and write all of off to save you all the grief.
Amy