A lot of the time there is no "correct" output.
E.g. a search result from a search engine is outdated the moment it has been generated - new pages come into existence all the time, and besides the index is unlikely to be up todate.
What matters is whether "close enough" is sufficient, and a large proportion of time it is: E.g. for the search engine example don't care if I get every single page that matched my query right at the moment I pressed submit. I care that I find something that meets my expectations.
Getting "good enough" results and getting them at a reasonable time beats not getting results or waiting ages because the system is insisting on maintaining global consistency.
Yes, there are cases where "good enough" means you need global consistency, but they are far fewer than people tend to think.