Without disagreeing with what other people have said so far, I must point out that it's unwise to pass judgment without knowing exactly where the guy is claiming to see continuity between the systems.
One specific claim I remember seeing ten years ago or so was that BattleTech uses the same volumetric tons (based on 1000kg of liquid hydrogen) that Traveller does. I forget the math on that, and whether it was supposed to relate to DropShips or BattleMechs.
If we were to look for continuity between the MechWarrior and Traveller RPGs, it's worth noting that character creation is only one part of an RPG, and the choice between life paths and pointbuy is only one part of character creation. You can't draw a meaningful conclusion without also comparing the ability and skill lists, how scores are scaled, how advancement works, and so on - not to mention travel times, communication, and other parts of play. For instance, I notice that MechWarrior divides equipment into Tech Levels, which is something I know Traveller also does, and I have to wonder if Traveller's implementation is more similar (or, just as important for the question at hand, complementary) to MechWarrior's than the implementations in Star Trek or Doctor Who are.