That is not true and has never been true in the United States. Most Hotel law is based on English common law which includes the "weary traveler" doctrine. A "weary traveler" may not be turned away from public accomodations except for good reason. "Good reason" may include drunkenness or a well founded belief that they will engage in illegal activities. In recent years sodomy has lost its illegal status.
The Weary Traveler Doctrine originated in England where to turn a traveler away often meant that they were on the road at night and easy prey for the many robbers or worse. They were also at the mercy of the elements. An innkeeper had to have substantial and valid reasons to consign a traveler to those dangers. This concept carried over into our public accomodation laws. It was no accident that civil rights lawyers went after hotels and restaurants first because the basic precepts were already embedded in the law.
Property is a bundle of rights and responsibilities and an innkeeper's responsibilities are broader than those of the general populace.
First of all their is no law in the United States which supercedes the Constitution not even English Common Law.
But to use your own argument against you, the whole point the hotel owner made was that they could not habitate the same bed. If they wanted to rent seperate rooms or a room with seperate beds no problem. If they were to tell the owner they were going to sleep with each other regardless then the owner does not have to rent to them since they insist upon breaking the owners rules. Why must a gay person aspouse to everyone in the world that they are gay. There wouldn't be a problem if they wouldn't have said they were gay and just rented seperate rooms.
There are several states which still have laws making homosexuality illegal, North and South Carolina are two of them. They are just not enforced by the politicians because they are afraid of the special interest groups and not interested in doing what is right.
A very good example of this is that there are several communities throughout North and South Carolina that in order to live in the housing development you not only must be a Christian but you must attend the communities church and if you don't you are required to move. This has been taken to court several times and each time has been upheld by the courts. One other note is that in the community in which I live their is also a hotel that is owned and run by the community. In order to stay in the hotel you must state that you are a Christian and are not gay. This hotels rules have also been upheld in court.