I'm in the "not necessary" group. You're not relying on the hydraulics to hold the car up, and as long as you're not fully emptying the cylinders they'll back up the mechanical/physical structure holding up the car. You don't have jack stands to back up your jack stands do you?
To answer your question, I'd put the stands in place to hold the QuickJack if you can. In the highly-unlikely-if-set-up-correctly scenario where the QJ fails, you've got a better chance of catching it in a stable and secure spot on the car - they're more likely to get knocked over, etc. However, I think positioning that is going to be complicated and risks damage if you forget the stands are there, etc. Tires are more likely to be a good buffer, but they're going to make ingress/egress even more challenging since the QJ precludes getting under from the side...
I hate jack-stands, and my paranoia would drive me to have a couple of jacks in place as backup and/or a tire or two tucked under the car. I hate them, hated putting them up and never felt entirely safe under the car.
I have the opposite feeling about my QuickJack - as long as I've done things right, it's entirely safe.