I'm not going to back up the claim about ZSS being on the same level as Marth/Wario because
-I wasn't the one to make that claim
-I don't even thinking Marth and Wario are on the same level
That said, I don't really know the ZSS:ICs MU in-depth but I can't think of a ZSS other than NR who would know the MU as well as he does, or an ICs other than ESAM who would know the MU as well as he does.
AFAIK there are no ZSSs with whom Vinnie gets regular practice, and Vinnie has been known to make a few wild claims...I also asked him in the chat of a stream quite a while ago and he said the MU was even, then a few months later he beats Salem at COT6 and suddenly it's -1 for ZSS XD
All that said, I'll explain the MU to the extent of my knowledge.
ZSS is very good at staying safe on shield. Dsmash, bair and sideB are all safe on shield (this is important because even when ZSS is landing while trying to juggle Nana, she can just bair a Popo who tries to start a dthrow CG and then continue the juggle), and since Nana's ******** she can easily get hit by these even though Popo shields them. Once separated Nana gets absolutely destroyed, even if the ZSS messes up you know Nana is taking at least 50% because ZSS' air game is ridiculous. Coupled with the fact that Nana's high in the air when separated, is a stupid CPU that doesn't know how to DI or momentum cancel and you have Nana dying at like 70 or 80 to an aerial sideB.
On top of that, ZSS also has 2 useful meteor smashes to gimp Nana and/or Popo offstage, in her upB and downB.
Furthermore, both ZSS' neutral B (laser) and sideB outrange Blizzard.
Furthermore, with ZSS' dsmash it becomes hard for ICs to recover and they usually have to resort to a high Squall Hammer (that's their sideB, right? XD) to recover, because if ZSS times the dsmash properly she can dsmash Popo out of Belay. Not to mention that dsmash and bair will go right through Squall Hammer and you have ICs offstage once again. This becomes especially hard with just Sopo because you can just react to a Squall Hammer landing with walk-->dsmash/pivot dsmash.
ZSS can also shield pressure well with spaced bair and sideB.
ZSS is also very good at juggling and ICs suck at not getting juggled...ZSS is faster in every aspect (running speed, rising speed, fall speed, horizontal air speed) which means she run away from Popo pretty well to destroy Nana, or to just chase them both while they're in the air and juggle the crap out of them. Yes, uair EASILY outranges ICs' dair XD
Also suitpieces kick ***. That's all I can think of right now.