When they say they used AnyDVD, that means "AnyDVD is what it was used to bypass the encryption".
The other program, DVD Shrink or CloneDVD or Nero Recode,their use is inferred, they are just not mention because is a given that you need to use one of them in order to author your DVD, shrink it, remove unwanted audio/subtitle tacks. Then you use whatever you want to burn the DVD.
However, you can rip the DVD to your hard drive only using AnyDVD if you wish so, as AnyDVD has a built in ripper now.
As Cyprus rightly said..
People are probably referring the fact they used AnyDVD to rip a DVD to
their HD, and then used another program like DVD Shrink, Nero, etc.. to reencode it and burn it to a blank DVD.
It cannot by itself backup movies but it can rip them to your HD.