Seth Grahame-Smith added to the original and he included Jane Austen's name because had he not it would have been plagiarism. That should tell you something.
The inclusion of Austen's name on Seth Grahame-Smith's book had to do with the fact that he used exact phrasing from Austen. There's a cottage industry of fiction derived from Austen's novels, including books like
Mr. Darcy, Vampire, that don't give a byline to Austen because they don't use her exact words.
If you have an interest in the topic of plagiarism and intellectual property rights beyond posting about it here, let me recommend Thomas Mallon's
Stolen Words. He discusses the psychology of the plagiarist, and he has an interesting final chapter about a lawsuit involving Earl Hamner's
Falcon Crest series. Hamner was accused of ripping off Anita Clay Kornfeld's novel
Vintage. Ultimately, Hamner won the case because it was demonstrated that both works relied on standard characters and plot devices associated with the family saga, and earlier works were actually cited as a shared inspiration.
In the case of Austen and some of the horror texts, films, etc. that have been mentioned in this discussion, one or two works eventually inspired a whole genre once they were allowed to come into the public domain. If you don't allow derivative works to exist at some point, then the arts would've died centuries ago.