Besides cutting knives, I have seen it done with cutting wood boards, and the outside of cooking pots.  I was told once by a Chinese friend that you do not use the outside of cooking pots, so why waste detergent, water and time cleaning it.  And yes, one knife to cut fruits, one for meat and fishes, and one for vegetables, and at the most a quick rinse under a bit of water.  No soap and water at all.

And even if clean, they still wash dishes and cooking pots (inside only) prior to every use.  Hard to understand or find a logical explanation, maybe they do not like the soap residue they could claim will stay with the knife after a good cleaning.....

Why wash it when it will just get dirty again the next time you need to gut someone on the bus and take their iPad.

How did you know they dont wash it? They do! Just  hygiene radar isn't as high as some of us.   

Part of the answer is the distrust of chemicals, which is what washing uo liquid is seen as. They do not want chemicals in their bodies. That is how it was explained to me by a Chinese friend of my wife. After five years of marriage and thanks to the colder weather I am just getting my wife to accept warm water is better for washing up than cold.

I haven't seen this at all...just the opposite.  My Chinese friends tend to clean their pots, pans, knives and the like very, very diligently.  I am amazed sometimes at how much effort I see them putting into it ... far more effort than I extend.

It is true that most of the times the dishe are washed and rinced in cold water, but then again, cold water is used in the washing machines here almost exclusively.  It is my understanding that their dishwashing detergent and laundry soap are made for cold water washing / cleaning.