Maybe they have broad pools/categories where some people on the WL are grouped in tiers, where some are on the higher end of what they want to accept but may not have room for and such, and review from that pool first (which technically isn't ranking, at least, not individually). Maybe they do a holistic review or look back on everyone and it's an ongoing re-review/decision process (unlikely, but who knows). Maybe they look at the current demographic of their class, and re-evaluate who they can bring in to increase diversity, in which case ranking doesn't help them much. Maybe they draw names out of a hat!
Obviously all speculations, but I guess my point is that there's not just one system, and if they say they don't rank, it doesn't necessarily mean they're lying. I think diversity is a focus point for Tulane, so if I was a gambling person, I'd put my money on that (also important to note that if I was a gambling person, I'd also be largely in debt ... well, more so than current student loans).
Well, my opinion is, I think it's a really huge assumption to say that there's a ranking set in stone, and updates can't change that. They urge you to send them any updates that you feel will enhance your file, so if there is something then why not? But I also don't have much insight on the behind-the-scenes admission process, and you might, in which case that would be useful information!