I'm not so sure the shooting your own foot analogy applies. Bitcoin could save WU millions in infrastructure (if they discarded their incredibly antiquated network and switched over to the blockchain, for instance). And the overwhelming majority of the population of the planet does not have access to the items necessary to obtain bitcoins themselves (access to the internet, the ability to transfer money into and out of an exchange, a way to securely hold the coins and so on).
If you assume that Bitcoin isn't going to die any time soon, piggybacking onto it might just be the smartest thing Western Union and Moneygram could do.
This. By integrating Bitcoin WU is saving itself from going to obsolete. Adapt or die. Bitcoin is here to stay.