DrChinese,
I admit that I don't know much about GHZ. However, in the article by Zeilinger e.a., Nature 403, 515-519 (3 February 2000),
Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement, I found the following quote:
"However, we realize that, as for all existing two-particle tests of local
realism, our experiment has rather low detection efficiencies.
Therefore we had to invoke the fair sampling hypothesis21,22,
where it is assumed that the registered events are a faithful
representative of the whole."
So, at least on the face of it, fair sampling is used in GHZ experiments. Of course, the article is relatively old. However, in the following article (GHZ and Shimony, Bell's theorem without inequalities, Am. J. Phys., 58 (12), 1990) I found the following: (the authors discuss a possible GHZ experiment):
"The second step is to show how the test could be done even with low-efficiency detectors, provided that we make a plausible auxiliary assumption, which we call fair sampling. Finally, we show that the auxiliary assumption is dispensable if detector efficiencies exceed 90.8%." So it looks like you need 90% efficient detectors to do without fair sampling in GHZ. To the best of my knowledge, there are no such optical detectors. Please advise if I am wrong.
As for your latest reference (12.4 km experiment), the authors seem to be remarkably reticent on the issue of absence/presence of loopholes.
Another thing. At
http://www.quantum.at/fileadmin/Presse/2008-07-01-MG-PW_A_Quantum__Renaissance.pdf Aspelmeyer and Zeilinger (Physics World July 2008, p. 22) write the following:
"But the ultimate test of Bell’s theorem is still missing:
a single experiment that closes all the loopholes at once.
It is very unlikely that such an experiment will disagree
with the prediction of quantum mechanics, since this
would imply that nature makes use of both the detection
loophole in the Innsbruck experiment and of the
locality loophole in the NIST experiment. Nevertheless,
nature could be vicious, and such an experiment is desirable
if we are to finally close the book on local realism." Then they discuss GHZ and do not claim that a loophole-free experiment had been performed. This article is recent, unlike the 1998 article in arxiv that I quoted before, so it looks like I did not misrepresent Zeilinger's opinion.