After Mr. Howell moves into the Skipper & Gilligan's hut & kicks them out, they are seen trying to sleep on the ground. The Skipper & Gilligan are discussing how to take possession of their hut again. Skipper says, "Gilligan, THAT is OUR hut!" As he says the line, a hut is shown in the frame, but the hut that is shown is the HOWELL'S hut, not the Skipper & Gilligan's.
When Skipper says to Gilligan, "That is our hut!", the camera shows the Howell's hut because the door curtains are orange.
Marriage certificates determine the legality of a marriage, not religious personages who oversee the ceremony.
If the minister who married the Howells was a fraud, the Howells, living together as a married couple for over twenty years, would be married according to common law. (Note: The Howells were old-fashioned, and with their standing in high society, Mrs. Howell in particular was concerned about appearances).
The Skipper and Gilligan completely overlook the fact that after their hut is taken over by Thurston and Mrs. Howell moves in with the girls there is a free hut for them to sleep in, namely the Howell's. (Note: everyone was trying to get the Howells back together, so leaving their hut open was essential).