I posted about that in the "issues" thread. As far as I know, that's not an option that you can turn off in any of the settings. In fact, I'm almost positive it's a stock Samsung option, which is the only thing I absolutely hated on this phone.

Are you sure the setting that you unchecked is for that and not the Preview in the status bar?

Anyhow, only resolution I found is to get this app:
https://play.google.com/store/apps/details?id=net.everythingandroid.smspopup&feature=nav_result#?t=W251bGwsMSwxLDMsIm5ldC5ldmVyeXRoaW5nYW5kcm9pZC5zbXNwb3B1cCJd

When you install that app, just go into settings for that app and you'll see the option that'll prevent your screen from waking up on every text message. The app works like a champ and my phone hasn't woken up for any text messages, since I first found out about the app.

Why Samsung didn't add an option to prevent that in the settings is beyond me.

Also, I turned off my text message notification sound and have SMS Popup running the sound, just so that there's no possibility that the Samsung software would override SMS Popup.

 

Hey Drex, can I use the above app but still use the stock sms app as my primary all the while eliminating the screen on "feature"? Call me crazy but the stock one is good enough for me except for the screen on annoyance.

 

The app DrEx posted isn't an SMS app.
It's only function is to stop your screen from waking every time you receive one.

 

Yeah, it's a SMS app, but it's not a replacement text messaging app entirely. I'm still using the OEM text messaging app in conjunction with it. I'm only using SMS Pop-up for text notification and to prevent the screen from turning on.