You may be right.
If there's a doubt or an ambiguity, then I'll bet both claim to be the first. What I've read lists LDS.
There's also the possibility that YMCA can make the claim because it sponsored BSA Scouting, while the LDS struck a deal to have a distinct Scouting program called "LDS Scouting."
It's not unusual to have different Scouting programs in a country; most European countries have several different Scouting organizations based on religion, labor unions, or distinct area of the country.
Has Romney disavowed this position? I would like to see a link stating that he is no longer for gays in the Boy Scouts.