I have those tires. No problems. I have had the kind of fall you've had on a MUP, but that wasn't my tires' fault. Instead, I hit the side of the pavement at too sharp and angle for the size of the skinny, high pressure tire and thus hit the side of the wheel instead of rolling up onto the pavement. My guess is that the base of the grass was lower than you thought.
It's hard to tell from the pic and I know that Specialized doesn't always paint the most symmetric stripes on their tires, but are you sure it's installed squarely on the rim?
Other things that could contribute to your feeling of stability involve your bike fit, such as your seat position, stem length and stem angle, and whether the frame is the right size for you.