G-4's have pretty small nose gear tires. The plane had a heavy fuel load due to the flight plan, so if one tire failed, the weight/speed of the plane may have over stressed the other tire. Maybe the tires were older, or previously damaged? If there's a cut, and it's on the ramp side of the tire, you wouldn't see it on a pre-flight inspection. They could have also hit something on the runway, causing a tire to fail. They did the right thing(s). Burn off extra fuel because G-4's can't dump fuel, then divert to some airport that's an old/former SAC base, with a 12,000' runway, and set it down, slow & nose high, for as long as possible.