This is absolutely untrue! A good webmaster will never build a site for a specific resolution and while some sites may become weird when stretched, most people do a nice job making sure this isn't the case. Unfortunately, most people nowadays use windows (where windows are usually maximised) and larger monitors are also gaining popularity fast, so it is wrong to claim sites are designed for 1024x768. Designers usually use one of these 2 options:
If you really want a fixed size site (usually because of graphical elements that don't allow stretching), you can do that by making white space appear on both sides of it while the content remains in the center and is reached just as easily as it would be in a non-maximised window.
The other option is to have your website (along with the content) stretch, which is the usual practice. This may probe a bit awkward in a couple of cases (as you pointed out), but usually it is more of an advantage. If I'm reading a discussion board, I want as much content as the screen can handle on it. This simply means I can have more posts displayed at the same time and I can read more content without having to scroll.
EDIT: While writing this post, I had my Firefox browser window maximised and I noticed it doesn't get streched like the screenshot above shows. It is more of an Opera bug/feature, which further proves the point some of us are trying to make.