While they both start with the same data, minor copy errors during DNA replication will eventually mean that they are not 100% identical. The odds of both twins actually mutating in the same way is actually pretty low. Most of these copy errors will occur in the womb, however some can be attributed to environmental factors.
Normal DNA tests take a few locations of the genome and compare them. To be more thorough, you test more points. Eventually you'll find a difference that you can use to compare. It's like comparing two books. You open to the first page and see the same acknowledgement you might assume the same book. But sampling a few more pages and you'll realize that maybe one is partially plagarised from the other.
They should pay it just to show that 'twin' crimes are not uncatchable.