I was thinking about this for a while after reading it, and I think I know what the science is.
If you think about it, the weld is probably limited by the steel can side, not the nickel side. If we reference the conductor current rating sheet,
9.8A of current through steel can be poorly carried by a strip 0.3mm x 7mm, which has a cross section of 2.1mm^2. This is about 4.67A per 1mm^2 of steel. If we look at the size of a weld, I measured about 1.1-1.2mm in diameter, which has an area of around ~1.1mm^2. So 1.1mm^2 of steel multiplied by 4.67A = ~5.13A. I figured the poor/hot number made sense as the 5A rating for a weld was a max.
This is just a hypothesis and could be completely wrong.
One thing I noticed is when you compare it to the other current ratings of steel strip, it does not really scale. Seems like the bigger the strip, the ampacity increases is nonlinearly. Maybe because of different heat dissipation or something.
Also the area of a circle calculation for a weld is radius squared so it can vary a lot based on weld quality. A 1mm diameter weld is only good for 4A based on this, but a 1.3mm diameter weld can do 6.25A.