Is it possible that the weight/balance determination for the first flight was incorrect, but that with less fuel the cg was in an acceptable range? If the same, incorrect, cargo weight/distribution data was then used prior to the ill-fated takeoff it might have shown the cg to be within range with more fuel when it actually was not.
Hell no!! I have been missloaded and overweight many times (only finding out enroute and after landing). Twice had to divert for fuel, once unexpected rotation probably 15kts prior to rotation speed, just about on V1. We were severely misloaded. None the less the W/B would be caught in FMS trend data on the previous flight and would not have an effect large enough to catch on the first flight, severely disruptive. Hell the life of a freight dog, check your cargo.