With all IVs at 31, yeah those people definitively cheat xD
Best you can have in the last game for a legendary one is 3 IVs at 31 (shiny or not, the shiny just depend about how much you reset, for example, I got a Shiny Terrakion after 1277 resets xD) but then it's not impossible at all to have a full shiny legendary team, it's just awfully time consuming xD
Do you have a retail game to test in classic mode, to see if the whole emunand is banned? Would be curious to know if the whole system is banned or just emunand (as emunand have a different friend code if it's unliked). If yes, the fix would just to have a backup before the ban then restore the emunand?
If it's a system ban directly with a unique ID/serial, then nothing can be done, of course.
Well first pokemon only have 6 stats and max IVs don't mean you will just lose. I know how to use gateway to make pokemon and let me tell you, it doesn't work that way. You can manually set the stats but they won't let them go online if they don't pass a check.
Also if you play rating battles a chunk of legendaries that are stupid strong are banned.
All IVs at 31 are authorized, as it's pretty easy to get legit.
About EVs, they shouldn't overcome 510, which is the official limit, or they are refused from what I read.
So, you're right about the fact that hacked pokemons can't be better than legit ones.
For the battles, I think he talks about randomb battles, which follow Nintendo rules so no pokemon bans. You can only use rules with someone that know them.