Not necessarily.
Consider this situation: you hire a contractor. They work for you for several years, and then you fire them. The contractor goes to the labor court in their country and files a claim stating that, yes, their contract says that they are an independent contractor, but no, since you've employed them "full-time" for several years continuously, they are a defacto/de jure employee. (Which is a valid argument under the labor laws of certain countries)
What will you do:
- Spend the time and money refuting their claim? (You need to find a good lawyer in that foreign country; lawyers are expensive; and someone on your side needs to spend their time coordinating with them)
- Ignore the claim? (Not a good idea if you ever want to visit that country in the future)
The claim itself might be nonsense; that's immaterial. You're faced with a Hobson's choice if said contractor drags you to court.
(Addendum: this is why I made the point that labor law is local. When you hire a national of a foreign country, in general, you subject yourself to the jurisdiction of the courts of that country for labor related disputes.
I am not sure if a clause in an employment contract stating that the agreement is governed by U.S. law would be accepted by a local court; and even if it did, in litigation, you'd most likely have to represent yourself before the local court to make that objection.)