I'd also add that another approach could be joining the local organization as a volunteer, and helping to get a system in place for annotating existing data. There are many positive aspects of offering monitored annotations of a public record, including helping to bolster membership by encouraging the public to return to an online posting.
Inspired by the tools at Ancestry.com to annotate their online records, I sent an email to the main historical society in Wisconsin to request corrections to a state government index. I was amazed by their positive response; they were happy to make the changes because I included proof of inaccuracies in the published index - which is different than claiming inaccuracy in the records themselves.
Having said that, in later submissions of corrections, I successfully argued that the original interpretation of the spelling in a hand-written record could easily be reinterpreted.
In the local genealogical society, I've recently come across the attitude by a board member in charge of research services that the concept of spending time to offer corrections to posted information was outrageous.
I really do think of it as a personal ethics question.