To correct a misconception, Twilio works with a variety of carriers, including Level3 and Bandwidth.com. Much like Google Voice, we work with a plurality of vendors for redundancy, geographic coverage, etc..
Voxeo also works with Bandwidth.com. "Bandwidth.com shares Voxeo's 'All-IP' worldview and as a result is an important voice network partner for us." --Jonathan Taylor, Voxeo CEO
I believe Twilio integrates directly with a single carrier (Level3). Last I checked they use/resell bandwidth.com for most of their calls.
-Jonathan (Voxeo CEO)