The knife-cut seems to work over a seemingly very small cross-sectional area, which says hugh resistance. Presumably the colossal pressure melts the conductors, which equals a really good conductivity, lower resistance connecting. Just squeezing one wire against another might not actually have that much contact cross-sectional area as the conductors might not actually be touching closely over the whole of that apparent area, and the conductors might not melt together so well, or at all. The knife-cut method also involves two changes of metals, A-B-A. This isn't ideal but unavoidable presumably, as Cu-Cu-Cu would be too soft, and the knife blade link material absolutely has to be really hard.
Does any of that speculation sound right?
[Actually, apologies for going completely off topic, unless we can say this is relevant because it's all about lowering total end-to-end resistance.]