There are four groups of people:

A - "Philadelphia is the capital, and others will agree."

B - "Philadelphia is the capital, but most others won't know that".

C - "Harrisburg is the capital, and others will agree."

D - "Harrisburg is the capital, but most others won't know that."

This technique eliminates groups A and C from consideration, and measures the difference in size between groups B and D.

Both groups B and D think they know something other people don't, but B is wrong and D is right.

In cases where people feel like they have "inside" knowledge, generally speaking it's because they are correct and knowledgeable (group D), not because they are misled (group B).

You often arrive in group D by virtue of having been in group A and then learning the actual truth of the matter.

You can arrive in group B by falling prey to a conspiracy theory, which makes this technique perhaps invalid in such cases? I wouldn't be surprised if the question "Do vaccines cause autism?" had a surprisingly popular answer of "Yes".