Fonts are defined in the style sheet (template) of the website and that's so that you don't have to worry about them. Doing this helps keep the website looking professional and uniform - versus having too many fonts going on. Another advantage is that if you want fonts changed on the whole website, you only need to do it in one place instead of going into each individual page.
An issue with fonts is that for them to work well on the web, people need to have them installed on their computer, so there's only a limited amount of those fonts available that work on all computers - see this page:
There is a way now to send fonts (font faces/styles) through the website. It's called embedding fonts. We're now doing this on some websites that we've built. If this is done, then a default font from the list above still needs to be chosen.
When using fonts on the web, you don't want to go crazy and have your website look like it's a MySpace page that a teenager made. It should look professional and be easy to maintain. By taking font control out of the equation, you have more freedom to add content to your website and not have to worry about you or anyone else at your company having to maintain any style guidelines. Your company looks more professional.