I think that you are not referring to the right reason why your former students cannot simply go on and publish the small projects they did under your supervision in lower-tier (let me guess, author-pay) journals.

It's not that *the work done in the lab belongs to the PI and the lab as a group*, it's that **you and possibly other people in your group contributed** to these projects, at least by providing scientific guidance and supervision. 

As such, **they cannot claim that the work is solely theirs** by not mentioning you as co-authors and, as a corollary, cannot publish without your explicit consent.