Interesting. I'm an American, and once sustained a bloody but minor scrape of my knee when playing basketball in China. I went to the campus clinic/dispensary to obtain some bandages, since I couldn't find any that were the right size at the nearby convenience store; there, the staff practically tried to admit me, telling me that I had sustained a very serious injury and that I needed to take it seriously and start a course of antibiotics. After an awkward conversation concerning my refusal to take antibiotics without (what I deemed to be) sufficient cause (being mindful and wary of the resistance risks of an unnecessary course), and their belief that I was being disrespectful of their medical expertise, I left with a bottle of antibiotic pills that I never took. My knee was as good as new in a week or so.

Point being, medical cultures can differ quite a lot, even from locality to locality, and the differences can be seen even in the handling of minor scrapes.

In China it's much more common to take antibiotica for minor reasons.

Also big (area wise) skin wounds can get infected even if they are not bleeding.

Correct me if I'm wrong: I think that a wound that is bleeding is a wound that's, at least in part, being protected from infection by 'internal positive pressure'.

My grandpa taught me that; to let wounds bleed freely for a while, if possible, to reduce the chance of infection.

I wonder how valid that is.

Sounds plausible. At the very least it's a mechanical cleaning. Small pieces of dirt get washed away by the liquid blood.