The question is how binding a decision of a US court would be for a Swedish company, negotiating according to the employment laws of three different countries.
IANAL, but you'd be surprised how binding decisions in courts in various countries are on other countries. Generally if you do any business at ALL in a country, court decisions are binding (frequently for example Canadian companies seize assets of US ones who think court decisions aren't binding on them and vice versa). If you get a judgement and a company doesn't comply you're just asking for someone to get a seizure writ (that's what they are here in Canada) and enforcing it on property located in CAnada, for example, but the US is fairly similar. You can for example seize a plane, and sell it, to get back your money, though a judge would probably want you to be a bit more reasonable. . .