Data usage with data turned off

My daughter's phone is talk and text only, so it has the data turned off (we learned this because she is using my old phone and the data was on...turned it off after about an hour).

It still seems to be using a bit of data on a daily basis, though. Small amounts, such as 0.1MB on one day, 1MB on another. What could be causing this? She is arguing that texting where there isn't WiFi will use data, but I don't think so. What can I check? We've checked several times that data hasn't been turned on and it's always off, so either something is turning it on and off, or there is another problem.