Earlier quoted context omitted.
The relationship is causal. Married couples are a household. Married couples consist of two people. Two people is more than one person. Two incomes is more than one income, etc. Even though all married households are not dual income, those that are shift up the mean for the rest. This is an artifact of measurement via 'household'.
You've missed rayiner's argument, which is that the household income is more than the sum of the median man and the median woman. That is: two married people make more than two single people. There are a number of arguments you could make as to why (for example: married people tend older and so are farther in their careers), but it's not just "married households have two incomes and single households have one".
Sure I didn't say it was the only explanation. But it is a sufficient one to prove the relationship is causal.