Scarlett, I see that you are reading the Australian news again! Good work! 'Get through the net' is a metaphor in this sentence. It means that only the 'real' students, who qualify to do a course, can join the course. All the 'fake' students, who shouldn't be joining the course, can't 'get through the net'. They can't get into the course.

"Get through the net" x > It is actually " Slip through the net/crack " , which means getting pass something unnoticed or caught .Its an idiom , meaning it must be said in this way to be correct. So, you version is just a "copy" of the original. I don't think the usage in your phrase " only genuine students can slip through the net" is good . Because , this idiom is about "catching" rather than "allowing " > has put significant recruitment measures in place to ensure that fake students cannot slip through the net (and get themselves enrolled)