When you have a shallow skin abrasion, it often doesn´t bleed. The lymph that seeps out doesn´t flush too much either.
Allowing a small wound to bleed a little is Ok. Forcing the bleeding doesn´t add a real benefit. You simply can´t create a flow that makes enough difference. I´d be really careful with puncture wounds. It´usually hard to tell how deep it is. The rubbing may well help to make the infection worse.
When the skin wasn´t broken with your acccident you may have suffered a small bruise. In that case increasing the bloodflow actually makes it worse.