I just heard from a guy last week who had a fairly new chain and clip master link fail on him. The link plate (with the pins) of the master link snapped, the clip popped off one of the pins and the chain came apart. He was lucky, it happened in his driveway as he was leaving for a ride and no damage was done to him or the bike.
When I was recently researching what chain to buy to replace the worn out cheap chain I had, I found that most every high end street chain comes with a rivet master link. Some manufacturers offer an optional press fit master link, and very few offer clip master links, and I didn't find any quality O or X-ring chains with clip master links, even as an option. Again this is for street use. A clip master link is nowhere near as strong as a riveted master link, and has too much play, so what is the point in buying a chain rated at 9000+ lbs tensile strength if the master link is only good for 4000 lbs?
Off road, it doesn't matter as there isn't enough traction, on the street there is and it does.