Lol, every time I hold Ax suited on Pokerstars, the flop comes also suited but allways another suit then the one I am holding. Probably not true, but it is a pattern I 'discovered' and since then, I see it happening much more often.
What I am trying to say is, if you start to notice a pattern on a site, you will focus on it and see it much more.

If you read in the newspaper about a certain type of car being the topseller last year, you suddenly a lot more of those cars on the road, just because you start to focus on it.

I think the reason why PKR shuffles twice, is because true randomness doesnt exist. No machine can provide you with 'real' random numbers because it allways needs some seed to derive the numbers from.
PKR uses the previous random shuffle as seed
Pokerstars uses 'user mouse movements' and 'thermal noise enthropy' as seed.
Full Tilt does a continuous shuffle and picks the card when you click the button. Clicking a microsecond later will give you another card, very frustrating if your opponent hits his one-outer.