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You should not be blaming verizon for this. If the data can turn on, then ask Apple why OS5.1 is doing this.

I dont see how verizon could be doing anything.
 
I've been in Mexico for the past week with my Verizon iPad and not once has it turned on. By the way I have it in an airplane mode with Wi-Fi turned on.
 
Due to the massive data usage of this thing I have been much more closely monitoring my data usage and I have noticed that when you go to check your account in settings, it will turn on the cellular data even if it was off before hand. I will notice it says Verizon at the top left even though the slider does not move to ON. If you go to another part of settings or exit the settings app and go back in, it will show as ON.

Here is a screenshot right after I checked.

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Even once you clear the box it still does not move to ON. It is only after you leave that part of settings and go back in. (yeah, the screenshots are out of order, I realized I needed to download an editing program so I could edit my number out to show the first one)
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I just did this and it turned on my data plan. I think it does this when ever you access your account because you need to have a connection to sign up. I remember it did this on my other AT&T iPad. When I wanted to sign up for a data plan, it automatically showed a 3G connection to allow me to enter the information to purchase the data plan. It didn't turn on my data connection anywhere else on my iPad. Only when accessing my data plan account...just like it did on my AT&T iPad.
 
I could understand turning it on while you access your account, (though if you're on wifi, there no real need) but it should show up as being on or turn back off automatically. As it stands now, unless you see the Verizon in the status bar, you have no way of knowing as the slider appears to be off.
 
I haven't had it happen again. Weird. I was aware that the cell service will turn itself on when you check your account and I agree, if it can turn itself on for this, it should turn itself back off.
 
I think it does this when ever you access your account because you need to have a connection to sign up.

This. It turns on when you access your account. It will not manually turn on at any other time.
 
Thanks, I've been tearing my hair out for the past hour because I just subscribed to the AT&T data plan (250 mb) on my new iPad 3. I only want to use the cellular data on my next trip should WiFi not be available, so I disabled it. But, it seemed to be re-enabling itself, which could use up my 250 mb quickly. You're right, accessing the plan, to check the settings, usage, etc., does turn it on rather than using WiFi to retrieve the info. Unfortunately, it doesn't turn itself back off when done. Live and learn! Obviously, I'm going to closely monitor those bars in the upper left corner to make sure they say iPad instead of showing the signal bars.
 
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