I don't have access to any specific information per type or design. However, the AMM statements regarding the cross vent check valve and ambient air are a bit baffling, and perhaps even mis-stated by the Boeing tech writers. More information on the center tank venting design may be necessary.
While climbing, the tank must be able to vent overboard to maintain ambient pressure. If you seal it up, there will be a serious problem with structure in fairly short order. Likewise, during descent, it must be able to draw air in so that ambient pressure can be maintained. Finally, as the fuel volume decreases, air must be introduced to fill the volume.
Unless the design concepts have changed, (and I haven't been involved with this for a number of years), the nitrogen is introduced in order to reduce the oxygen content to around 10 to 15%, which pretty well negates combustion. The problem with the nitrogen supply is that one needs to have enough to replenish the ullage during the climb/descent dynamics. This was one reason the military nitrogen systems that we first looked at were considered inadequate, as they provided nitrogen only during the short periods of combat exposure, not during a long haul flight.
I can see a system which is closed while the pressure differential between tank ullage and outside is static, such as on the ramp. But in the end, there is no way to really trap the nitrogen throughout the flight regime without introducing the enormous problems associated with a pressure vessel as a fuel tank...