A claim can be made if married couple's allowance is due because one party was born before 6 April 1935. This also applies to civil partnerships, and to cases where one spouse is claiming not married couple's allowance but blind person's allowance.
It is a question of relative incomes, not whether a wife does not work and a husband does. If the article was couched in those terms, it was most misleading, especially given the age requirement (one spouse needing to be over 73 now).
This link and thereabouts may help, although the guidance is quite tortuous: