I've found that to be pretty typical. Our issue when we were looking into rescues was we were automatically denied because we're a military family despite having had our own dogs with no problems. I understand their reasoning but should be a case by case basis. Its possible the rescue may be willing to work with you on the fencing.
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Shasta GSD 5/5/10 CGC, ITD, TC
"Dax" Thor z vom Weberhaus CAX, CGC, ETD, HCT, RATI, RATN, TC 3/18/2013
Zena GSD 6/1/03
Riley GSD/BC 1/10/05-2/1/2013