1. It was stated in the manga, 'cause is stated in the databook too. And Kishi wrote the databook too.
Um, no. If it was stated in the databook, then it was stated in the databook. It doesn't mean it was stated in the manga too. It's also obvious that there is significant inconsistency between the databook and manga. From Itachi supposedly having the same genjutsu ability to Oro (both are scored an equal 5), to Ameratsu being described as "hot as the sun" (yet barely affecting Karin), to the recent timeline catastrophe (see the manga forum), which is even worse if one uses the databook ages and timeline (caused by the sudden desire of Kishi to claim that Tsunade and Hashi knew each other, thus destroying the previous timeline by years). The databook was not written by Kishi, though he got input, and Kishi sometimes contradicts himself, so the idea anything Kishi ever looked over becomes cannon is ridiculous (Kishi clearly changed his mind about the relative strength of the 1st and 3rd Hokage, even if it was never explicit... likewise, the indirect remarks that Hiruzen "knew all jutsu in the leaf" are plainly wrong, even only going off the word of Kishi, because to take but a single example we're also told only the 4th and Jiraiya could perform Rasengan). When Kishi got input to the early databook, he hadn't even invented the idea of elemental balance, or how they fit into blood line abilities, etc, yet we're supposed to assume stuff that was written (by the same company for which Kishi works) is always valid, even when Kishi changes continuity frequently? (who could forget Gaara suddenly becoming a host like Naruto, clearly not what Kishi originally intended). Um, no. The databook is never to be cited reliably. Ever.
2. The Tsukuyom, for example, i is a different story... I know that can't be broken with chakra control. I'm talking about the regular genjutsus and about the regular sharingan genjutsus.
So you get to arbitrarily pick which genjutsu can be broken by Tsunade, and which can't, based off no evidence whatever. Sorry, it doesn't work that way. The evidence doesn't support you (see eg's above), and the fact that you love Tsunade is not an argument. Here's how feats work- if characters don't demonstrate said abilities...
they don't get granted them.