Verizon informed me today that no app, not even the stock Data Usage feature can turn off your Mobile Data. If you wish that your data be disabled at a specified level, you must now add Family Base to your plan. Not sure if that is fair or not, but Verizon has decided to do so which is their choice. I am a bit skeptical though: Google disabled apps' permission in Android Lollipop to enable/disable mobile data out of security concerns, yet somehow Verizon is able to get away with it.
Who did you hear it from, sounds like a sales pitch attempt, was it from someone higher up or just customer service type?
I already knew Google's part in the restrictions, but I didn't think that a feature that Google put into the phone would really be a part of the apps that were restricted, given it was a Google feature. But, sure enough, once limits are reached, a notification comes up saying your data has been disabled, but the 4G LTE keeps on flowing and the icons stay lit up. I was on chat earlier today, alas the screenshot is not permitted here. A lot of my info can be proven, but Verizon TOS won't allow me to post given its nature.
Definitely very sketchy, I like to set my limit above anything I would hope to hit but would hopefully catch/stop any rogue app that perhaps decided to use copious amounts of data before it costs me hundreds of dollars.
EXACTLY why I liked My Data Manager or at least the stock built-into-Android Data Manager to control data in case runaway apps racked up data. My Verizon app can tell me the most up to date amount used, but it doesn't update in real time and must be opened and refreshed each time. MDM counted text/mms as data, but kept me in check since Verizon would state I used less because text/mms don't count against data (unless you use VM+) and the phone counter is a bit off and sketchy itself.