I think there can be a certain crassness about facebook sharing of any kind really but it has also become part of the way that we communicate with people. I wouldn't personally share lots and lots of pics of DC on facebook (mainly because of their own right to privacy) but one or two snaps of family holidays or whatever maybe.
I have been snide about someone sharing pictures of their sunday lunch (again) or people being vague but can't imagine being critical about someone sharing a picture of a sick child.
I know though that my networks are quite big and it is impossible to keep up with everyone without FB. Ex colleagues, current colleagues, old school/college/uni friends, sports friends, people from the community where i have lived, where i used to live. I have shared parts of my life with these people at different times, and currently, with many still do. I love that facebook has helped maintain a feeling that these people are still current and made it easy to keep in touch when everyone is busy.
I know if one of their DC was ill i'd want to know, if i was in that position, i'd want to feel people were thinking of me, and I know that they would care.
I think if you have seen a picture of someone's sick child on facebook and that your reaction is to think 'how crass', they are not really someone you care about. Maybe you are not using facebook in a way that is helpful to you.