Perhaps the pairing shown above happened toward the end of SERENITY.
Maybe River Tam wasn’t the only one in that room against the Reavers.
That might explain why River Song later on took on the Miranda P(?) aliases.
Moreover, maybe the Order of the Silence, under Madam Kovarian, were responsible for the creation of the ultra-secret organization known as Blue Sun.
And through Blue Sun, The Silence were perhaps able to kidnap and condition young River Tam into the perfect weapon against The Doctor, just in case Melody Pond (River Song) failed in her mission.
Lastly, Badger could be the descendant of Canton Everett Delaware, III, who other than being a smuggler, might be acting as a double agent for the Time Agency, instructed to keep tabs on Ms. Tam.
Meaning that there might be something to this picture: