Data inconsistencies will always sneak in unless you're vigilant.
SQL data stores provide a way to limit certain kinds of inconsistency, but a) I rarely see a system that uses all of that power, and b) there are plenty of inconsistencies that you can't prevent with standard SQL features.
Personally, I'm ok with schema-less stores in the same way I'm ok with saving files on disk. I don't expect my filesystem to enforce application-level file format quality. I just expect it to store things and give them back when I ask. That doesn't mean I don't care about data integrity, it just means I solve the problem somewhere else in the system.