I read an article somewhere where Cindy McCain was interviewed and she said that she and John McCain had made a real effort to try to keep their kids out of the spotlight, especially Bridget because she was the youngest. Apparently they were both extremely hurt when the rumors were spread in 2000(possibly by the Bush camp) that she was his illegitimate child. This is one of the main reasons that McCain and Bush have had a not-so-great relationship, to put it lightly.
She also said that they fear for their sons especially, who are serving in the military...that they might be targets because of who their father is. In an interview in Time recently, the reporter asked some sort of question about their sons serving in the military, and he responded "I'm not discussing them."
My guess about the whole adoption thing...as far as Cindy just saying she brought Bridget home and asked John if he wanted to adopt her and he said "yes" and then they did it....this seems easier than trying to explain to a reporter the craziness of adoption paperwork and processes that all of us have come to understand.
Michele