When you watch REMEMBER THE TITANS you will see that the students arrive in yellow school buses. In fact the students were bused in public metro buses. I know this because my mom went to T.C. Williams and the yearbook shows this!
THe movie has MANY differences from what really happened. Just about any movie that is based on a true story doesn't necessarily recreate only real things. There were characters specifically created to dramatize events and ideas. Your mother, having supposedly attended the school, would have told you that.
Rev didn't really break out in song. Actually, Rev wasn't even called Rev by his teammates. The team did not dance on the field while warming up. The restaurant owner didn't really deny them of dinner--- but it reflects the mentality of people in that era.