https://www.reddit.com/r/AskHistorians/comments/3j51hw/carbon_dating_suggests_worlds_oldest_koran_could/cumcu6m Basically, yes, they only tested the paper and also carbon dating isn't laser accurate, especially for newer items being tested.
Decay rates are statistical averages, correct. In this case 5700 +/- 50 or so years. For those who don't understand this, if I had a bucket of C14 that weighed 10 pounds, in roughly 5700 years I would have a bucket that weighs very marginally less than 10 pounds (E=MC^2 converts a very, VERY small amount of mass into energy during radioactive decay) but would be 1/2 C14 and 1/2 Nitrogen-14 (N14) If we sit and count the atoms at this point we should expect to be close to 1/2 and 1/2. This is why there is an error bar on any radiocarbon dating.