On Verizon's website, you can change your account settings to block data entirely. I've done that for my girlfriend's phone, she doesn't need it, doesn't want it, and just blocking it was the easiest way to prevent accidents like that.
It's pointed out explicitly in the article that such action does not work.
Feel free to try the following:
Have her hit the button.
Don't hit End; let the phone do its thing and reply that you don't have data access.
Consult your monthly bill.
