An easy way to avoid this website picture rotation problem
I think I figured out how to get around the rotation problem on this website. The website's picture manager doesn't understand EXIF information about picture orientation that you get on high-end cameras and iPhones. So, it displays them in what it regards as the native format, which is landscape. No doubt this comes from the way the JPEG array reads out: row by row, but a portrait picture needs to be read column by column and the website picture software can't do this because it doesn't read the EXIF information.
Some people have suggested using Camera+ on an iPhone to take the picture, since it presumably doesn't use the EXIF approach. The problem is that this won't work if you've already taken the picture with the iPhone's native software.
The solution is to edit the picture in some software, such as Preview on a Mac. For example, crop it slightly. This causes the JPEG array to be rewritten in a format that the picture editor understands.