I perused the Site as I have not looked it over. I am not a customer of theirs but I do sell pearls online.
The things I noticed most importantly is in their guarantee section. They have a sentence that says they use a strict pearl grading system recommended by the GIA. This is big red flag because this is a lie. The GIA does not recommend any grading system, and there is no way they would recommend a AAA+ and especially not even call it perfect.
The GIA grading class gives value factors of pearls when assessing value. I guess the sentence that premiumpearl.com uses could be construed as assessing the value factors of a pearl, but they do not even use the actual value factors assigned by the GIA in their graph. I would really suggest you bring this up when considering a sale.