I've owned two flippers in the past and I now only own a non-flipper. I've never had the flipper accidentally open in either carry position. The flipper for the most part will require some wrist action. I really don't see a big deal about not use the wrist. Even though I was able to open it without wrist action, I had to concentrate on flipping it open just right. That required more effort to me than just using wrist action to be sure it opened every time.
There were two main reasons why I don't prefer the flipper:
1) when I carried it tip up (which I prefer in general), the flipper would scratch my cell phone in my pocket
2) The finger choil is small enough as it is. The flipper leaves less room than the non-flipper at the finger choil.
The main benefits that I saw the flipper having were:
1) Another option for opening, which I didn't really care about.
2) A finger guard
Personally, holding the non-flipper, I don't feel concerned about my hand sliding in any way. Secondly, I don't really see myself needing to stab something that hard to be concerned about it. I don't carry for self-defense, but even if I HAD to stab an assailant to save my life, I wouldn't be concerned with my hand slipping. It's not like I feel like I'll need to stab my way through a car hood one day. The day I start thinking that's a real possibility will be the day that I'll start carrying fixed blades for EDC.
All in all, I enjoy either version, but I prefer the non-flipper.