Of course you can keep things private if you choose to but that is really defeating the purpose of Diigo in the first place.
Diigo also began offering, on Sept 19th, a Diigo Education Account Facility. I haven’t investigated this yet but a post about it was put onto the SLAV Bright Ideas blog. It is worth looking at. From Diigo
‘The Diigo Educator Accounts offer a suite of features that makes it incredibly easy for teachers to get their entire class of students or their peers started on collaborative research using Diigo’s powerful web annotation and social bookmarking technology.’
For an educator account, you do have to apply and fill out how/why you want to use Diigo in your school.