I didn't double post. I asked a question about "system sounds and haptics" (this one) and a question about "ringtones and alerts," which has been deleted.
Setting the vibration settings to never (and then restarting the phone) did not turn of the haptic occurring when I switch the phone to silent mode. Are you aware that there are two categories of haptics in the Sounds and Haptics settings page? There are four options under "Ringtones and Alerts" and there is an on/off switch under "System Sounds and Haptics." As stated, I have switched that to off and the phone still vibrates when I switch it to silent mode.
I'll now repost my question about "ringtones and alerts" in hopes it stays up.