Obviously there's still some package running on stock Android and iOS phones. I'm going to assume it's related to the MyVerizon app.
I don't see how that's "obvious" at all. In fact, the article explains exactly how it's being done (packet inspection), and it's got absolutely nothing to do with stealthware hidden on your phone.
Verizon can monitor browsing, data, and app usage by monitoring data.
Log on to Facebook? Hey presto! You're sending API requests from documented Facebook APIs used in the Facebook app to a Facebook server. You don't even need deep packet inspection for that. Most apps connect with a server at some level to do something, even if it's just to get ads. And since they are on a defined ad network with a defined client ID, Verizon can tell what company is asking for the ad pretty easily, especially if they partner with the ad agency themselves in a reciprocal agreement.
Example: You play Bad Rodents Free (ad-supported). While you are trying to get your rodent through the maze, you see an ad for Bob's Plumbing from, say, AdEngine.
- AdEngine is in agreement with the developers of Bad Rodents. So Bad Rodents already used the "read phone identity" to get unique information about you to associate with the ad and sent that to AdEngine in return for a higher monthly ad fee, which pays for better rodent graphics.
- AdEngine kows that "a phone" from IP address 2.3.4.5 with known unique information from Bad Rodents requested an ad, and they returned an ad with an image ID of 123456.
- AdEngine contacts Verizon and offers money.
- Verizon can examine use the unique ID that Bad Rodents provided to associate your phone with you. Verizon can then add extra data - "the person who saw that ad was 25-37 years old, male, spends most of his time at Starbucks, and since you are paying an extra $20 to know about him here's his mailing address and a list of all of the contact information he foolishly used the free Verizon service to back up").
Absolutely none of this requires anything be running on your phone. All they need to do is a short sample of your "unique phone identifier" which if they don't have it from the get-go they can gather the first time you make a call or get a single packet from their Internet access point.
"Opting out" simply means you've put a "do not look" sign next to the ground-level bathroom window to keep the peeping toms out.