I need to look at our documentation to see what we did, but, no, our teachers cannot see other groups and/or submissions. Same w/ grades. I believe we changed Access all groups to prohibit http://docs.moodle.org/en/Capabilities/moodle/site:accessallgroups
This isn't just a FERPA issue. Separate groups considerably uncomplicates life for teachers. They don't have to panic when they are accidentally in someone else's group and phone me with "How did Joany Jones get in my class?"
I also use groupings to keep paysheets visible only to a particular teacher, the supervisor, and me. These are Google spreadsheets linked to from the classroom and hidden from students.