They're talking sh*te.
The logic does work WRT lowering temps, it does get you more power but only to a certain extent (I think it was something like 1BHP for every 5C decrease in temp), but obviously you can only get down to ambient plus a few degrees at best - so no it wont reduce it by 150F, maybe 60F. Also this wont flow more than the standard airbox, its quite well known that the standard airbox has plenty of flow. But in theory, with a good filter on certain cars giving more flow and lower temps can net you about 15BHP (Evos for example)