I use the Verizon Message app and I don't see any settings to disable. You can try a different messaging app. For example the LG stock app on Verizon models doesn't call on slide, however it deletes the message on slide.
Correct,
In order for the behavior to be different, you would need to try another messaging app. I like the Verizon one because I can link it to my IPad and make phone calls and send texts on wifi