Tier-1 without their own backbone?

We are sending out feelers for adding an additional DS-3, or possibly frac OC-3. One of the responses came back with "we won't be competive with <provider> because they don't have their own backbone. Is there a cross-reference for provider vs network backbone, or is this just something that we have to ask each provider for? I "assume" that UU, Sprint, and AT&T are self-owned backbones, but others... ? One of the providers we are looking at is Level-3. Any comments good/bad on reliability and clue? We already have UU, Sprint, and AT&T. I also realize that the "they suck less" list changes continuously... :) Thanks, Rick