Yeah, the stats are randomised each time. The Giratina I encountered in the Distortion World was non-shiny; however, in Turnback Cave, it was shiny.
By the way, if you know your secret ID (yes, you can calculate it without cheating, provided you've already caught a shiny Pokémon), there's not much point in SRing normally. You can exploit the predictable nature of the random number generator to get a shiny much more easily; it took me about half an hour to find Giratina, and I had to find it 4 more times afterwards (I failed to catch it the first four times). You also get to influence the nature and IVs (in this case, mine was Bold, with IVs of 29/x/31/31/31/22).