The iPhone and iPod, made by Apple, are products that compete directly with Microsoft's Windows Mobile platform and Zune media player. Bill Gates' children can no doubt get their hands on pretty much any Microsoft technology they might want.
I think it's a fair "ban," given Bill Gates' career at Microsoft. My father works for Eastman Kodak. When we still shot pictures on film, Fuji film wasn't exactly banned, but there was an unstated rule that we should buy only Kodak film. There's nothing wrong with supporting the company that pays your bills, or rooting for the home team, in a sense.
But apparently that sense of supporting the home team doesn't mean Mrs. Gates hasn't been tempted by the dark side. She also told Vogue, "Every now and then I look at my friends and say 'Ooh, I wouldn't mind having that iPhone'."