We're talking about the actual design of the site. I'm not one to get all wound up over definitions so please excuse if I use the wrong terminology here, I'll try to be as clear as possible.
A beautiful site can have an awful UI. The StartSSL site doesn't have that polished hipster-corporate look that we're so used to seeing these days. I think you might be talking about the experience. It's one thing to have a pain in the ass experience with forms or actions that require multiple page views/reloads to complete and quite another to have an ugly site in general. "Ugly" can be a very subjective thing though. StartSSL's site isn't exactly ugly but more dated looking. Speaking striclty from a design point of view, without being overly critical, the site is aligned nicely, has a nice grid, the typography isn't fancy but it's not so ugly that you'd complain about it on first glance, the colors are okay and don't hinder readability, there's enough white space, etc. Even so, when it comes to design there are always those intangible qualities that you can't quite describe or put into objective terms (which I'm sure is very frustrating for programmers as we're all about exact, measurable, science-y stuff).
So considering that the site isn't ugly from an objective standpoint, how could it still be ugly? To answer that you have to take into account experience. Web design, much like fashion, has fads and trends. Right now we're used to seeing what I like to call "hipster-corporate" design. This style is all about being casual while still looking corporate enough for people to take the comoany's site seriously. It's really tough to straddle the line between trying too hard to look hipster-corporate and looking dated and old fashioned. We've all seen the website for the local doctor's office that looks like it's trying too hard to be that big corporate style but failing miserably and looking like the crappy free Wordpress template that it is. Hipster-corporate is really interesting because there are a lot of variations and the amount of hipster style or corporate style that mixed in all depends on the company's personality and size. Too much or too little of one or the other totally breaks the feel.
So the point is, after all that, I think we're talking more about the "feeling" that the site gives you rather than the objective reality of things when we talk about the site looking pretty or ugly, good or bad, well designed or poorly designed.