This is largely true in the US. I can't speak for how it works in all states, but in most you need an official to marry the couple. The official can be either a religious minister or a government official (such as a Judge or Clerk). From the States point of view, it is not really a religious issue.

There are actually "religious" organizations who for a small fee will give you a certificate to act as a minister to perform a weddings, no dogma required. I believe these are accepted in all states.

In my state of Colorado, a couple can marry themselves without the need for any official from the state or religion. Couples marrying themselves are free to ask a friend to stand in as an informal "official" during a ceremony, but legally, they sign the marriage certificate as having married themselves.

In the US the question of gay marriage is really about the government recognizing the it and giving gays and lesbians the legal rights and responsibilities found in marriage. Most church's will continue to be against it and not perform such ceremonies. Although a few, such as my own Unitarian Universalist have been advocating for gay marriage for decades.