I actually found a way around this, if you guys are interested.
Since Siri can only read text messages if the preview is enabled on the lock screen, just go ahead and disable it.
Step 1: Settings > Notifications > Messages
Step 2: Show Preview: On
Step 3: View in Lock Screen: Off
This way, nothing will be visible if you don't want it to be, and you still have the convenience of jogging or driving and having Siri read your messages.
Not the the perfect solution, but it works, if you're interested.