You're talking about rooting which is different from sideloading.

On android, you can go to foo.com/someApp.apk and after accepting a bajillion warnings, install the app with no approval from Google needed

Isn't this thread talking about sideloading APKs, not installing custom ROMs?

https://www.verizonwireless.com/support/knowledge-base-22218...

You don't need to mess with the bootloader at all to sideload apps on Android. Maybe you're thinking of installing custom ROMs?

You don't have to only use Verizon branded phoneson Verizon's network. I haven't for years.