I don;'t know where the Samsung CS people are located, but most Verizon CS people are located in a different universe.
When you have the TV set to the Chromecast input (my Vizio switches to it automatically if it receives a signal - unfortunately, it doesn't switch back when I turn Chromecasting off), and you run the
Chromecast app and tell it to cast to the Chromecast you want, it mirrors the screen. Any and all apps now appear on the TV screen, including the homescreen.
There ARE certain apps (like Chrome, Firefox and Youtube) that can Chromecast without mirroring the screen, but they don't do it as well, or as easily, as the Chromecast app.
This is from what I've been doing for over a month. I have no idea what Verizon or Samsung are talking about. (Verizon usually has no idea what they're talking about either, which is why I've tried them 3 times and dropped them within the free period.)
The reason there are apps that Chromecast on their own is that not many phones can use the Chromecast app to mirror yet (see
Chromecast mirroring for a list).
Step by step is - set your TV input to Chromecast. Run the Chromecast app. Press the 3 bars at the upper left. Press Cast screen. Choose the Chromecast you want to cast to. (It comes up even if there's only 1.) Watch the TV screen.