EUSA is funded with a £2.3m annual grant from the University and the clause has been inserted in the condition of grant. The Scotsman's account of the circumstances is here.
Free speech is, of course, a paramount consideration. Yet also important is that EUSA is funded by public money. EUSA, which exists courtesy of such public funds, does not have the unfettered right to use those funds to do and say anything. I note the clause only requires EUSA to give notice of publishing anything 'detrimental' - and does not prevent the expression of such views.
Postscript 22.10.13: According to this report, the University have now backed down and dropped the requirement