The reason for using EAC is that the error correction on audio CDs is barely enough to ensure a perfect reading under perfect conditions. The Red Book specifications envisages error correction failures, and says that in this case, the audio should be interpolated.
Reading an audio CD in a CD ROM drive, two factors can push the reading out of spec.
1- The reading speed, that is much faster than specified in the Red Book, thus likely to cause more errors than envisaged. It is itself at the limit of error correction. In order to get the fastest reading possible, drive manufacturers allow the drive to spin as fast as possible without errors on a perfect CD. Any less-than-perfect CD will thus have errors. The drive should then decrease the reading speed until no errors are got. But all this happens at the edge of the error correction ability, and some can pass through.
2- The CD state. If there are little scratches, or fingerprints, some parts can't be error corrected. Some CDs can also be defective to begin with. Many burned CDRs of poor quality can't be read without errors, etc.
The test for C2 accuracy had nothing to do with me. It's a program by Andre Wiethoff, available under the DAEquality section of the
http://www.exactaudiocopy.de website.
What I did was using it to perform extended C2 tests. This is in a specific webpage :
http://perso.numericable.fr/laguill2/dae/dae.htm