Well that hack check is as follows:
You battle someone, save the battle, and post the battle video.
If it says:
"There appears to be a problem with your pokemon" => Meaning you had hacked in your team.
"There appears to be a problem with your opponants pokemon" => Meaning your opponant had hacked pokemon.
Now to be sure to identify the hacked pokemon. What I do is I battle with 2 pokemons; one of them is a wild caught bidoof/magikarp so I know those arent hacked and the second one is the pokemon I wish to check for.
Although many hacks can pass the GTS, it is always good to check it.
How about you trade me your Uxie?