Because when you apply reason and keep the foreign background of the students in mind you can very well arrive to conclusion #2. In Europe we simply don't have these sort of sensitivities, and stereotypes are often deployed for fun.
Remember Top Gear and the jokes about mexicans? Even the regulating body Ofcom cleared Top Gear of racism because "the programme frequently uses national stereotypes as a comedic trope and that there were few, if any, nationalities that had not at some point been the subject of the presenters’ mockery throughout the history of this long running programme." (source) Over here we have this magic ability to differentiate, which is why no one seriously thinks that mexicans are lazy, feckless, flatulent oafs with moustaches, leaning against fences asleep, looking at cactuses with blankets with a hole in the middle on as a coat. This sort of image of actual real mexicans simply doesn't exist in general, everyone knows it's a stereotype wheeled out for banter and fun. And I'm guessing that's also the case with the norwegian students here, especially the dirty part could simply have to do with the image of mexicans riding through the desert and arriving with dust covered faces. A typical stereotype.
Now as I said before, every country has its own taboos. You couldn't make this sort of joke about Pakistanis or Indians in the UK for example. And I understand that's the case in the USA with mexicans, which is why making these sort of jokes in the USA was stupid of those kids. I don't blame the OP for being angry, but I doubt there was ill intent on the part of the students or that the girl actually meant to offend with her "dirty" comment. Her real meaning could have simply been lost in translation.
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