As a side note to all the chatter on if using a fraternity facility is allowable, NPC also states that on campuses where chapters are housed, all NPC sororities must be provided with EQUITABLE housing to each other. DZ, at the current time, has none. Using this fraternity's housing unit gives them NO advantage. The house is well known, yes, so why would anyone question if DZ was living there now? Greek Life and NPC will make clear to the women going through the process that DZ is USING the ATO house...trust me.
hopeful, this is meant in the nicest way possible, but worry about your own recruitment. You have an awesome house, the biggest on campus as you said, and fretting over DZs use of a fraternity house is honestly the least of the worries. Focus those energies on making your own recruitment fabulous!