Suppose we are in a situation where no girls lie. Then each girl has a boy and a girl next to them. Looking at the adjacent boy, he must have two girls next to him. Continuing the pattern around the circle, we find that we have a pattern of the following form $$ G, G, B, G, G, B, \ldots$$ going all the way around the circle.
In particular, we find that there are two girls for each boy and the number of students must be divisible by $3$.
Now suppose we add a lying girl, then the effect on the pattern is either we have a section of three consecutive girls $$ G, G, B, G, G, G, B, G, G, B, \ldots $$ or we have a position where there is a "boy, girl, boy" section as follows $$ G, G, B, G, B, G, G, B, G, G \ldots$$ In the first case, the number of students must increase by $1$ modulo $3$ and in the second case the number decreases by $1$ modulo $3$. To make it simpler, if we begin with a $2:1$ ratio, girls to boys, then the first operation increases the number of girls by one and the second decreases it by one.
Since we have $3$ lying girls and $28 \equiv 1 \mod 3$, we must have two of the first case and one of the second which means we must have $19$ girls and $9$ boys. A realisation of this is as follows $$ G, G, B, G, G, G, B, G, G, B, G, B, G, G, B, G, G, B, G, G, G, B, G, G, B, G, G, B $$