I can see how they could have made an honest mistake

That's why it's always good to have a checklist so you don't leave out a step. Here's what my checklist said:

I. Requirements for an American to Marry in Korea

   1. Proof of U.S. Citizenship, such as a Birth Certificate, Consular Report of Birth Abroad, Naturalization Certificate or U.S. passport.
   2. A completed Affidavit of Eligibility for Marriage. (EA Form 737-E).  (4 Copies).
   3. A completed Report and Certificate of Marriage.  (EA Form 736-E).  (3 Originals).  
   4. Proof of identity: for example, a driver's license, military I.D., etc.
   5. Proof of termination of any prior marriage(s), including an original or certified copy of a divorce decree, annulment or death certificate for your previous spouse.
   6. If the American Citizen is under the age of 18, written permission to marry from both parents is required.

II.  Requirements for the Korean Partner

   1. Three copies in Korean and one in English of the Family Census Register (Hojuk Dungbon) issued within three months of the proposed date of marriage.  This will include Proof of Termination of any Prior Marriage(s).
   2. Valid Korean identification card (Jumin Deungnok Jeung) and name stamp (Tojang).
   3. If the Korean spouse is under the age of 20, written permission to marry from both parents is required.

IV. Getting Married in Korea

         1. Gather the documents listed above for each partner. Be sure to bring four completed copies of the Affidavit of Eligibility for Marriage (EA Form 737-E), three originals of the Report and Certificate of Marriage (EA Form 736-E) and documents required to get married.  (Do not sign any documents before you get in the Legal Office)
         2. Take the completed Affidavit of Eligibility for Marriage (EA Form 737-E) and Report and Certificate of Marriage (EA Form 736-E) to the Legal Office to be notarized.
         3. OR - You can bring all of the documents listed above for each partner to the Embassy.  The embassy will check all of your documents and notarize your Affidavit of Eligibility for Marriage.  The total fee for the notarization is $90 (no charge for military members).
         4. Take the 4 notarized copies of Affidavit of Eligibility for Marriage along with 3 copies of completed Report and Certificate of Marriage and W10,000 to your local ward office (Gu Cheong) for approval and signature by a Korean government official.
         5. Finally, bring the two copies of the Report and Certificate of Marriage signed at the ward office to the Embassy for authentication. The Embassy does not charge service members for this authentication. Make sure to take your military ID.

So, yeah. I find it hard to sympathize with the tiny amount of red tape that Irvin and Boyer had to contend with.

There are two questions here:  first, "Should anyone be allowed to form a legal domestic partnership?", and second, "Is there any advantage to having this institution if anyone is allowed to enter into it?"  I think the answer is "yes" to both questions.  I see no reason that civil unions need to be based on love or sex (although I would limit them to being between just two people, and only allow people to be in one at a time).  Say two sisters are in their 70s, are widowed, and live together.  Under current law they have relatively limited rights and would have to draw up a living will, give each other power of attorney, and so on, to even approximate the sort of rights that a spouse has towards his or her partner is a marriage.  Allowing civil unions would wrap up all those considerations into one legal action (getting the civil union) and would allow a person to say "from a legal standpoint, I implicitly trust this person to act on my behalf".  Right now the only real way to do that is through marriage - but if civil unions were allowed (and their context was divorced from sex, love or any religious meaning), these advantages could be made more widely available.  This is why we do need some sort of state sanctioned institution, though - there are many good reasons to give someone all the legal rights that married spouses currently have, and if we do away with that institutions entirely (from a legal standpoint), then we're back to having to draw up five or ten separate documents to try to approximate those rights.