It is a decision that every family has to make. It should be noted, however, that much of the "76 cents on the dollar" statistic has to do with work interruptions and reduced hours, which are often a consequence of being a primary caregiver. If the couple is a working mother and a SAHD, she should not have those interruptions (beyond maternity leave, of course).
(The other factor has a lot to do with career paths, and we could derail the thread and discusss whether societal roles forces these tendencies - that men gravitate toward higher-paying careers, because of the expectation that they will have to provide for a family, and women toward lower-paying ones, because of the expectation that they will not.)
Yes, this is exactly how statistics can be used to lie. I do not doubt that statistic about women earning 76 cents for every dollar that men earn, but too many people just accept that at face value and reach incorrect conclusions:
The work world is unfair to women.
There's no point in a woman really trying in the work world.
A husband can support a family better than a wife can.
The reality is that women earn less than men for a number of valid reasons:
Even today, women flock to traditional female jobs: Teacher, nurse, social worker, secretary -- and those don't pay as well as traditional male jobs: Accountant, Doctor, Engineer. No one makes women choose these jobs, although some of them are more family-friendly than some of the traditional male jobs. If we as individuals have chosen lower-paying jobs, we can't blame society for that. Most of the boundaries that held previous generations of women back career-wise have been erased.
Women do take more time off to take care of their families. A year or two off for the birth of each child. Time off 'til they begin school. A year off when a parent or grandparent is ill. Of course an employer will compensate his best workers, his there-all-the-time workers more highly. This isn't discrimination.
Women tend to change jobs more frequently -- sometimes because their higher-paid husbands get a job in a new place, and they have to give up their job and begin afresh somewhere else.
Other reasons probably exist too, but these things all add up to the average woman earning less than the average man. You should always be suspicious of statistics.