Advanced Shipping Rules connects as a calculated rate to your shipping zones in the Shopify shipping settings.
Shopify Admin > Settings > Shipping > Manage Rates
Below you see a two rates connected to the zone:
Ground Shipping, a native Shopify rates
Advanced Shipping Rules, a carrier service rate
The app has no access to the Ground Shipping rate
It cannot make adjustments to the Ground Shipping rate
It cannot combine with the Ground Shipping rate
When the app is connected to a zone it can only show rates at checkout, or not show rates at checkout.
As long as the native rate Ground Shipping is part of the shipping zone, it will always show at checkout as Ground Shipping for $12, and there is nothing the app can do to stop it.
The only way to stop a pre-existing rate from showing at checkout is to manually remove it from the zone