Yes, they definitely use BGP, however at that level, you don't necessarily have a "transit" (internet) provider, like normal ISPs do. You just peer with all the tier1s.
So, when Sprint (AS1239) depeers with Cogent (AS174), unless Cogent has a TRANSIT link with ATT / Savvis / Qwest / Level3 / GX, etc, the traffic will not flow.
Yes, you'd think they would have a transit link worked out just in case an entire AS blinked out of existence, especially when you expect it could happen, but they apparently didn't. That or their BGP filters on the transit linked filtered out anything for Sprint/AS1239 because of the peering link with Sprint. *shrug* Yes it shouldn't have happened the way it did - but there's many reasons why it could have.