I think it's different when you actually witness someone's crash. You don't know at that point if they are actually okay and of course it doesn't hurt to ask.

Last year I crashed pretty bad because my skinny tyres got in between the tram tracks as I had to emergency brake due to an unforeseen green light at the pedestrian crossing. I fell over my handlebars and made my knees into a meat crayon. A few people ran to me asking if I was okay. I was cursing at myself because it was such a stupid thing to do. So when asked if I needed help, I remember saying something along the lines "no thank you, I'm okay, I'm just stupid as fuck". So I proceeded to pick my bike up, pour water on my knees, put my chain back on, and left. Obviously I looked like shit, blood everywhere, but I was ok to ride home. I wouldn't have expected anyone to ask me if I was ok while I was riding.