EDTA chelates divalent cations which are required for nuclease activity. While the genomic DNA (gDNA) extracted using QIAGEN products, should not have any nuclease activity, it is possible to introduce nucleases during repeated long-term access of the DNA. EDTA helps to prevent any nuclease activity introduced after the genomic DNA extraction procedures.
However, if the gDNA is stored frozen at -20oC or -80oC, nuclease activity is much reduced. It may be possible to leave EDTA out of the storage buffer without negative consequences when samples are kept under these conditions, and when repeated freeze-thaw cycles are avoided.
We do recommend however that gDNA be stored in a neutral to a slightly basic buffered solution (e.g. 10 mM Tris-Cl pH 8.5 to 9.0) to prevent DNA degradation by acid hydrolysis. Note that deionized water mostly has an acidic pH.