Roaming and data are disabled, this happens if the phone is not being used. It also happens when he dials voicemail or sends a text. He is physically nowhere near the border. His phone is picking up charges on this, what are my options aside from switching to T-Mobile since Mexico is part of their coverage?
so long as you're in the U.S. you're not responsible for charges if the device connects to a tower in Mexico. if you see any charges appear on your bill call customer care. I'd suggest calling in and letting them know so they can document the account that way when it's time to remove the charges after the bill has been generated the transaction will be smoother.
I wouldn't want you to get a big bill and expect a credit, while you may have success in a partial courtesy credit due to one time/accidental usage, Verizon rarely credits any roaming charges, even in a case like this, and those charges can add up quickly. (Check out this site and others for such customer feedback/complaints that have had that experience)
From their terms and conditions site-
"If you are traveling near a country border, you may connect to a cell site located in a neighboring country and be billed at that country's rates."
Keep in mind your phone is a radio, so it will pick up the strongest signal possible based on the settings. So if someone is in a very rural US area near a border that doesn't have the best service and a foreign carrier does the device will be alerted of roaming, as well as a text advising of the rates, as well as overage charge text updates as more usage occurs so the charges would be valid.
The best way to limit extra charges would be to limit usage while roaming, turn the device off, or select a plan to cover the usage, even temporarily.
In my area we have a similar issue, due to our proximity with Canada. The phones will hop to Rogers wireless at the slightest sign of a usable signal, perhaps when the home network is having a blip. This can occur over a 24 mile long stretch of water, with almost nothing but the atmosphere and the shape of the planet to mess with the signal.
The most one can do is make sure the phone is set to avoid roaming charges on data and text, in addition to documenting for customer care (as pointed out above) these occurrences. Perhaps getting a basic international plan complimentary from Verizon will be a solution they propose to solve the momentary lapses of roaming.