This clause is to establish that the laws of the federal government (including treaties) are to have precedence over that of the states. It does not put the agreements established by treaty above those of the Constitution.
I'm not a lawyer, but my small dose of legal training says that the courts aren't going to be excluded when someone challenges a treaty provision as a violation of the Constitution.
Treaties are on the same level as all other federal laws. However, this means that they can't violate the Constitution the same way that Congress can't by passing unconstitutional laws.
I would probably agree with you as to how this is interpreted, but I was hoping some legal eagle would have a case in mind that the court actually agreed with that interpretation as well.
Sometimes the courts have done some weird things, like saying that you could take private land for someone else to develop for profit, and I would hate for that attidtude to bleed into other areas.
Oh well, I gusss I'll live with the mystery...
Or as Andy Jackson said, they have made their decision, now let them enforce it.