Well, there are several possibilities here. If your brother is a stranger to the teachers, then they may feel uncomfortable with his request. Teachers are totally responsible for the safety of their students during the school day, and allowing someone they do not know into the classroom is a scary idea, and it may actually be against school policy.
On the other hand - and I mean no disrespect to you or your brother, but I've been a teacher a long time and I've seen a lot of things - perhaps the problem is that the teachers do know your brother. If he was not a serious student in the past, or had discipline issues, then teachers may be responding to that in a negative fashion.
A third possibility is that the teachers are not actually empowered to give this permission; your brother may be asking the wrong people. I would suggest that your brother write a formal letter outlining his research proposal, and send it to the principal or the superintendent of schools, and let them make the connection to the teachers.