I don't know how the Co-op works. But a quick look at TSSAA and you can read it. And you can see Monterey has Co op program with Cookeville to allow them to participate in wrestling.
A cooperative program is defined as two or more member schools forming a single team in a sport in which at least one of the schools does not have a team and has not had a team for the previous two years.
The association office approves cooperative programs on an annual basis. Each year, schools wishing to participate in a cooperative program must notify the state office prior to the first practice date in the sport(s) involved.
When co-ops are approved the list below and the school's directory page are updated to reflect the co-op status.
If your school has students participating with another school's team and you do not see the relationship shown below then the agreement has not be approved by the state office. You should contact the state office as soon as possible to resolve the situation.
And two of the teams are on Yorks schedule every year.