Air basically raps a flex program so that you have access to OS functions through Airs runtime library, with Air 2.0 it goes a step further and allows you to target a specific OS ( native platform build). For what you want it seems there would not be a need to run as a desktop application as you will obviously be dealing mainly with a corporate database queries.
With the web based solution there is no need to worry about update distribution. I would be inclined to develop an app as you described with a web based solution. The nice thing about flex is that if you decide at a later date you need some desktop functionality you can simply convert the web based app to Air( a button click does it) and add the Air capablities that you want.
Flex is a free SDK. I hope the developer you're working with didn't buy it. Most likely what he purchased is Flash Builder, which is an IDE by Adobe that helps to build Flex Applications.
Flex can be used for two purposes, to build SWFs that are intended to deploy to a web server and played in the web browser's Flash Player Plugin. And to build AIR files that are intended to be run on the desktop.
AIR offers some additional features over web based apps, such as closer integration with the desktop.
For ease of deployment, I'd recommend building a Flex application; unless you think you'll benefit from some of the AIR specific features.
Short answer: you don't need AIR since you want this accessible via Intranet/browser.
AIR could very roughly be described as a replacement for a the Flash browser plugin, which runs standalone as an installed application (no browser needed).
Thanks much, folks!