I've played 120 hours so far.
Encountered about 2200 Pokemon so far, so says the statistics in-game & via pokesav.
The chance of meeting a shiny is 1 : 8192
I'm lucky enough to have encountered my first shiny pokemon ever (played since pokemon red) - a shiny Rhydon when i was at ~105 hours.
I somehow doubt that one with four shinies has got all of them 100% legit and catched them themselves. You would either have to be four times luckier than me (and with a shiny at ~2000th battle, I am already very lucky) or you would have to have no life at all and have played like 600 hours.
And i doubt even more than one would turn their ds on and off all the time to get a shiny palkia, with the chance being 1 : 8.192, meaning an average of 8192 on-and-off-turns (+-), proving that you never even heard of the world "life"
btw: you can check if your pokemon is legit via this very useful new tool & the help of pokesav's .pkm files:
http://pokeguide.filb.de/pAC/pac.php Note that this is a beta program, so some things might not work or may be false
so go check if your gts traded shinies are really legit