Here are the exact rules on figure skating costumes from ISU rule 612 from the current document on the ISU website:
At ISU Championships and International Competitions, the clothing must be modest, dignified and appropriate for athletic competitions – not garish or theatrical in design. Clothing may, however, reflect the character of the music chosen.
Ladies must wear a skirt. The Ladies dress must not give the effect of excessive nudity inappropriate for an athletic sport. Men must wear full-length trousers: no tights are allowed and the man’s costume may not be sleeveless.
Hmm, I thought ladies were allowed to wear pants as per a rule change a few seasons ago (everyone from Irina Slutskaya to Fumie Suguri did it). But maybe they changed that. I haven't seen a chick skating in pants for a while now, come to think of it.
Some further background on costume violation rules: At first figure skating had no rule about nudity and propriety in costumes. It was just a matter of tradition that everybody followed. However, sometime in the early 80's, I believe, the very buxom and high profile Katarina Witt was competing somewhere, and during a camel spin, she showed her camel. Let's just say the reeds on the river Nile were parted and baby Moses almost came peeking out. Monocles were dropped everywhere in shock. And a new rule about modesty in costuming was quickly implemented.
So how do figure skating's couturiers interpret this rule? Well it's important for the costume to showcase the character the skater is portraying. That's taken as gospel by everybody, and skaters who don't do enough of that will get friendly reminders by judges after competitions. And well, there's no nice way to say it (my favorite kind of thing to say!) so I'll just say it: a lot of the characters female skaters have to portray are floozies. Salome? History's most famous stripper. Carmen? Two timing tart. And you don't even want to know what the faun did in Afternoon of a Faun. Now obviously such characters aren't going to dress like sister wives on a fundamentalist commune. They're going to show skin and flaunt it. But wait, the rules also say the clothes have to be modest! Luckily for all, flesh-colored fabric came marching in like a naked but not actually naked knight on a horse. Now skaters get to have it both ways: portray a sexy character without showing any skin. And everybody was happy about that!
Except your roommate. And also every other time I post a figure skating pic (like this one of
Ashley Wagner) to non-skating fans they will freak out at me about how the tights/leggings go over the boot. I hardly ever notice whether leggings go over boots myself, but based on the reactions I've seen from not just people I know but non-skating blogs that happen to show a pic of skating, it is the thing that most concerns people new to figure skating. If leggings over boots were banned it might bring millions of new fans to the sport who would otherwise spit on it.
It serves to hold the costume together, to keep skimpy looking outfit on, to give an illusion of a flimsy costume with skinny strings and just enough cover-up with strategically placed decorations, while offering the athletes security to perform with confidence. 
