The curphy followership model says that individuals who are low in critical thinking skills and high in engagement are called "brown-nosers"

This is true. This model gives managers the ability to understand the types of people they will be leading, and bases it on the ability for a person to critically think about directives and how well the person engages with others. A brown-noser, in this instance, is a person who will not think critically about a directive, deciding to follow anything the leader gives to them, as well as engaging with this leader often, trying to get in their good graces.