Mattis, for example, had a relationship with the company while he was still working in government and had explicit communication with them telling them he wanted to help them get their product into the military.

Getting hired onto the board 18 months after retiring from government (possibly the delay was due to being distracted by getting onto military contractor General Dynamics' board) is the other half of the back scratching arrangement that powers the corporate-political machine that rules the country.

As to how they found him in the first place, presumably friends of friends of parents, their siblings, husbands, wives, etc. Her parents were in political circles in DC, they were good friends with CIA agents, father was an Enron VP, mother was a legislative director for some congressman. It's all very incestual in Washinton, kind of like old royalty.

A Stanford grad enters Harvard Business School after a year of “working” in Silicon Valley. After HBS, she joins an SV VC firm, never makes partner or does her own deals, but hangs on long enough to credibly assert a career in “venture capital” to those in mature industries who don’t know how to vet such a career. Excellent social skills with a unique ability to convey agreeability: a yes girl with flair. On two major boards.

I believe these people generally get asked to join company boards due to their network. In a way these people function as lobbyists of the company.