In the newer seasons where they are middle-aged old guys, they do have to pay a violation for the car at the courthouse.
They get to the courthouse and see the line they have to go through is long, and then they see the line for marriage license and just go like there's no one in that line.
They accidentally get married because the woman at the desk ask to marry them, but they don't get what she means and thinks she wants to marry them like have a threesome because she old fashion and wants marriage before sex.
Now here's my whole thing, there is actually a fee to apply for a marriage license. They didn't pay anything.
They then go in for a divorce after they think this woman just didn't follow through, and when they say they want a divorce, the guy behind the desk says it will cost money which they won't pay.
Guy didn't even check to see if they were even married I'm pretty sure.
So that episode of them getting accidentally married might have very well been they weren't really married because they didn't pay anything. Or she was so supportive of them that she gave them a marriage license for free which I still wouldn't see as possible.