<p>I want to be able to launch a third party process from within an Adobe AIR application (actually a command line process). Is there a security context that AIR apps run in that prevents this?</p>

Two of the most requested features for Adobe AIR have been the ability to launch native executables from an AIR application, and the ability to integrate native libraries into an AIR application. Unfortunately, neither feature is included in Adobe AIR 1.0.
However. Check out:
This blog post
Airaveer
Shu-player
Shu enables you to increase the power and reach of Adobe AIR. With Shu your AIR applications can quickly be converted into standalone applications to run on PC or Mac machines without the AIR runtime installed! Shu applications can also be run from a CD or network share and do not require installation.
  In addition Shu provides you the developer with a toolkit of commands to extend the system capabilities of your AIR application, features include,
controlling external applications, opening external files, database connectivity and control, system path retrieval and screen capture functionality.
Using any of these methods will however break some of the intentions with AIR, which is cross-platform development. And as far as i know that's the main reason why Adobe won't let you execute native code at the moment.