The confusion appears to be related to what's meant by "Personal Choice Dining." Here's Princess's definition from a <a href=http://www.princess.com/news/article.jsp?newsArticleId=na361> press release </a> issued earlier this year:
The program, part of Princess' commitment to offer passengers the opportunity to choose where, when and with whom to dine, is the only one of its kind in the industry that gives passengers a choice between a restaurant-style flexible dining option and a traditional fixed-seating cruise dining experience. (boldface added).
The bottom line is that you're participating in "Personal Choice Dining" on the ships that offer it, regardless of whether you choose open seating or traditional seating.