Give the guy a break - this is aimed at newbies.
Right - it is a no-brainer for us grizzled database developers. I can add a little constructive criticism though Tim. Your link table has an IDENTITY column - why? If you create a composite key of your fk_user + fk_group columns (check out your naming as well) and set this as the PRIMARY KEY to this link table you are killing a couple of birds with one stone.
(1) You have eliminated a redundant column
(2) You have ensured that you are not duplicating USER-GROUP membership (PK uniqueness)
(3) You can either eliminate your duplicate checking SQL and let the UI layer deal with an error, or simplify your checking to ignore the error completely