Another thing to think about is that the molar mass is a weighted average of the relative abundance of isotopes. Thus, even though Mitch correctly noted that we have set the mass of one atom of carbon-12 to 12.000... amu, you'll notice a periodic table for carbon reads 12.011. That's because there is a bit of carbon-13 naturally, thus the accepted molar mass is the weighted average of all the carbon-12 and all the carbon-13. Same for hydrogen. There is some naturally occurring deuterium and tritium, so the mass of hydrogen is not exactly 1.
So perhaps the mass is a bit different depending on where the relative abundance of the isotopes was measured?