I have a nasty scar on and under my left knee from a bike crash. We had a family get together about a month later and, being summer, I showed up in shorts. There were a lot of sideways looks but only one person asked; my mother. She looked properly disgusted at my answer, but that doesn't surprise me.
You know what's really embarrassing? Having to tell people your cracked tailbone, black eye, or dislocated shoulder is from tripping over, being head-butted, or knocked down by a dog. I'd rather say it was a bike crash any day.