Yes, and that is a case that should go to the Supreme Court and it will be upheld that if a gay couple is legally married in one state, they are married in all states regardless of if it is legal for gays to marry in that state or not. They didn't marry in that state, they married in a state where it was legal, so the state cannot refuse a license that was issued from another state.
The only thing I could see is if the document states that they are married in the State of Iowa, for example. However, the state could not issue one license to straight couples and another one to gay couples because of the 14th Amendment and the equal protection clause as that would NOT be equal under the law.
Edit:
Neolibs, sorry, but it sounds like the law that Clinton signed is unconstitutional. Congress and the President have no legal authority to state that the Constitution doesn't apply to something.
Keep in mind that I am a conservative Republican and base my opinion on nothing but the Constitution and the writings of the Founders at the time the Constitution was being debated. For example Madison directly addressed the issue of legal documents in Federalist Paper 42, discussing that the Federal government would insist on reciprocity in legal documents as it deals with things such as commerce. As marriage does have interstate commerce implications, such as insurance and inheritance issues, and bankruptcy issues, which is also specifically addressed in the same document, whether you or I like it or not, Article IV Section 1 has to apply. Personally, I am NOT a fan of it, but it's there and has to be dealt with in accordance with the US Constitution.
Edit
Paula, I see what you are talking about there, however to go along with that argument means that the Supreme Court never makes mistakes. I think they have proven time and time again that they do. The Dred Scott Case is an example. Another one is Brown Vs. Board of Education. "What? You are saying that the Supreme Court made a mistake in Brown Vs. Board of Education?!?! You racist pig!!!" Hold on. Brown Vs. Board of Education demonstrates that the Supreme Court can recognize when it has made errors in judgments as Brown Vs. Board of Education was actually a REVERSAL of Plessy Vs. Furguson saying that school segregation was legal.
A legal document is a legal document. The primary purpose of a legal document is to define a relationship and establish it within the rule of law mostly dealing with commerce, including marriage contracts. No one can make a case otherwise as marriage contracts have very tangible financial consequences from property rights to insurance contracts.