Taking credit for others effort is an offense and punishable under the law. These centers should refrain from such malpractices. Just to protect their business they can not cheat the public.
Knowledge is power.
Also, they can't be reported as they are partly telling the truth.
Don't sweat the small stuff and it's all small stuff.
Sometime back I had a different experience. A boy from a school we never joined any coaching centre obtained rank 4 or 5 in the entrance test, Then one big corporate college approached the parents. They offered him free education next two years and they will advertise as if that boy studied that class in their institute. They offered him free boarding lodging, dresses and all expenses for the next two years and the parents accepted. This is another method of claiming ranks from their institutes. All business tactics.
On the other hand, many students (or their guardians) also play different tactics to ay hefty amount to those coaching institutes. Students (or their guardians) contact different book stores after taking admission in those coaching institutes. They get good amount of money allowing these book-stores to photocopy the study materials and notes. In this way, they partially get back the huge amount paid to the coaching institutes. The book-stores then earn profit by selling these study materials at reduced rate to other needy students. In Delhi, this tendency can be seen.
Caution: Explosive. Handle with care.
'Idhuvum Kadandhu Pogum "
Even this challenging situation would ease