Fyi...
I just signed up for Verizon Wireless with an iPhone 5 earlier this week after switching from an iPhone 5 on another provider. I just noticed that I used cellular data today and I've been at home with a STRONG WiFi signal! I have noticed the times I appear to be using data is immediately after I bring the phone up to use it after it's been sitting around in sleep mode or idle for a while. It's as if it was in some power saving mode with WiFi off and then I turn on the phone and I immediately see "LTE" for a second or so before showing that I'm connected to WiFi. This is strange because, well, I thought I was on WiFi the entire time. I would like to point out that I also use two Apple Airports (Extreme and Express, both updated) for my WiFi at the house. My iPhone 5 is also updated to iOS 6.0.1 and the carrier settings are Verizon 13.3.
Regardless of what's really taking place, I just got off the phone with Verizon (and Apple) and this is what they told me to do:
1) Reset all SETTINGS. Not just network settings, but ALL of them. ONLY SETTINGS. Test to see if you're still being charged data.
2) If resetting all settings doesn't work, then restore the phone and set it up as a NEW phone. Do NOT restore from a backup, which is what I did when I switched to Verizon.
3) If those two options don't work, I was told by Apple to get the phone replaced at my local Apple store. Yes, REPLACED. As if it's hardware related (I doubt it).
I hope this helps. I haven't tried this out yet, but I will try it out now and report back shortly.