"Exposure" by Eric Frank Russell (first published in Astounding Science Fiction, July 1950, available at the Internet Archive):
"Their simulation was perfect. They had the power to lead us right up the garden path if only they'd known how to use it. Power is never much good unless you know how to use it. They made a first-class blunder when they grabbed their models." He scratched his head, eyed the other speculatively. "It sure beats me that of all places in this wide world they had to pick a nudist camp."
"Solar health center," corrected Kampenfeldt, primly.
