Perhaps I misunderstood. The tool shows any ads on political and social issues, which should cover all the ads you mentioned (e.g. Exxon, Koch, insurance cos.), but won't cover Jellop ads.
Perhaps I'm being cynical, but my impression is that FB is aiming to provide just enough information that people will say "they're doing that already", and not enough that people can really understand what's going on. But I might be wrong.
The Ad Library claims to show all active ads, not just political/social ones. That's presumably true, but hard to verify or make use of. The "Jellop" ad that I couldn't find was missing precisely because the page name was something else they'd created for that ad.