Ideally, it is true that COMPLETE information makes an economic system work better..... but the improvement isn't some sort of linear progression, where every bit of more information adds a bit more economic efficiency. Sometimes, getting more information without getting ALL the information actually hurts economic efficiency.
A very easy example of this is wikileaks and the elections in 2016. It appears that wikileaks received information about both the democrat and republican parties; however, they chose to only share the information they recieved about the democrats.
By your assertion, we should not be concerned about this; after all, the information that was leaked was true, and therefore added to our overall body of known information, we should have been in a better place to make an informed decision, right? More information is better!
However, this isn't the case; because the information was selectively released, we only got the information that benefited one side, meaning that our overall understanding of the state of things actually DECREASED as more information was released.
This is the same thing happening here; you know Allstate isn't going to be looking for social media information that HELPS your claim. They aren't going to say, "Well, we were going to deny your claim, but we found from your social media feed that you were clearly really hurt. We have decided to pay out instead!"
Basically, if the extra information you receive is being selectively given by someone who has an agenda, you can be mislead even if all the information is true.