I don't pretend to be a carb guru but, removing a restrictive filter most definitely leans out the saw. Think about it this way, The carb is tuned to deliver a set amount of fuel at the maximum airflow available at WOT. If you remove the filter or change to a freer flowing unit, you take away an air restriction, increasing available air. If you do not retune the carb accordingly, it becomes a lean mixture and rpms will go up as the carb is only capable of providing a set amount of fuel. Saw carbs have a very narrow window where they're happy to start with so making a significant change on the amount of airflow will make a pretty noticeable difference in the way it runs.
I will agree that more airflow through the carb will pull more fuel, that is the basic concept behind how a carb functions. However, it can only provide as much fuel as the carb is set to provide at a specific amount of airflow.