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."