I was taught the same. To not care a lot about things under an order of magnitude. Over the years when planning large software projects or assessing incidents and so on, the 1 order of magnitude threshold helped me often.

As a physicist, I think this is correct too :). You don't start to see problems with things under that, unless they are deviation from standard model predictions.

Variance in accuracy of this statement also safely within one order of magnitude

An order of magnitude isn't a defined quantity, it depends on what base you're working in.

In this case transferring the data at the slow rate would have taken more than a week, so it's no small difference. Actually one side had a 10 Gbps line, so if the other side had had faster networking I could easily have exceeded the limit and gotten the transfer done more than 6x faster.

I used the term "1 Gbps line" just because it's a well known quantity - the limitation of Gigabit Ethernet. The point wasn't that multiplexing TCP can get you 6x better speeds, it's that it improved the speed so much that the TCP bandwidth-delay product was no longer the limiting factor in the transfer.