How the hard drive makers provide URE values?

It turned out that vendors of hard drives provide information on URE out of the blue. This URE data is commonly utilized to substantiate bogus statements like “RAID5 is dead ” and to guess probabilities of double read error in RAID5.

People who build their own RAIDs are starting to get nervous seeing these values. But the vendor URE data seems to be lacking proper reliability.
Have a look at Hitachi official website, they specify sort of exciting URE values for 3 TB hard disk – 10^-14 errors per bit read.
Let’s suppose that the value is real. So, if you take this disk and start to read data off it from the beginning to the end then the probability not to encounter a read error will be:

(1 – 10^-14)(8*3*10¹²)~0,79

therefore, the probability that the hard drive wouldn’t be able to read one sector is about 20%.

In other words when you have a disk filled at capacity there is a significant chance (namely 20%) that you will not be able to get data off it.
This is clearly disproven by everyday practice.