It seems to be a mistake of the writers. In fact, a double mistake.
Firstly, in the book Deke and Mimi indeed married, but the book Mimi wasn't Afro-American, so there were no obstacles preventing the marriage.
Secondly, in the TV show there was no mentioning of Deke and Mimi being married. In fact in episode 6 she said quite the opposite:
-You believe me when I tell you I love Deke and he loves me?
-Deke and I have spent our lives next to one another. Not with one another.
In addition to the above, in the book Jake's memory loss after being beaten is much more severe (chapter 26). For a long time he doesn't remember Deke and refers to him as A Man In A Cowboy Hat. When he finally recalls who Deke is he uses a very similar line to the one cited in the question.
It is of course possible that Deke and Mimi married secretly, in another state or in fact never married and Jake only thought so due to his amnesia.
However based on the above book information the most plausible theory is that the writers made an error during adapting the source material. It seems that they used the line from the book without realising that not only the marriage didn't happen in the TV show, but also that legally it wasn't even possible.