Of anyone I know

The American Heritage Dictionary reads

Anyone is often used in place of the more logical everyone in sentences like

• She is the most intelligent person of anyone I know.

In our 2017 ballot, the Usage Panel accepted it 55 percent to 45 percent, while rejecting the supposedly correct alternative

• She is the most intelligent person of everyone I know.

69 percent to 31 percent.

Presumably an idiomatic reading, “compared to any single person I know,” outweighs the literal reading “out of all the people I know.” The implication of a one-by-one mental comparison may explain why the expression survives.

However, I find the explanation contradictory, because the meaning "of everyone I know" is also on the lines of “out of all the people I know.”

Also, I can't fully grasp what the author means by a "one-by-one mental comparison."

The anyone/everyone difficulty is interesting. If John is the tallest of the group of everyone I know, his height exceeds that of all other members of that group. That being so, his height exceeds that of any one of the group; he is taller than any one of the group.

This argument leads to the notion that he is the tallest of everyone, and taller than anyone. These alternatives read well but when applied to intelligence the proper use of comparatives fails us. To say He is the more intelligent of anyone ..., although logically justified, is ungrammatical, inelegant or pedantic. GJC makes a good suggestion about this inelegance - it would read better as "He is more intelligent than anyone ...". The Heritage Dictionary folk seem to have overlooked the most/more, tallest/taller issue in their discussions.

If I make a one by one mental comparison of all those I know, my mind ranges (or at least tries to range) over each of them so as to select the most intelligent (or whatever quality is in question). It is rather like the physical comparison of looking at a city skyline and selecting the highest building, but no such physical line up of intelligent people is possible so it has to be attempted mentally.