Haven't seen the mathematics of failure re-stated for some time, so...
Multiple studies in US, Germany and Japan, at least, have found levels of XMRV in the healthy controls varying 2-7%. Assuming from these results a modest background infection rate of 3%, the probability of a study using a test that can detect XMRV in human infection finding none at all in a random population sample of N=104 would be 4.2% (1 in 25):
(0.97)^N
In the case of the CDC Western Blot on plasma alone, N=104 (53+51)
3%....(0.97)^104 = 4.2%
4%....(0.96)^104 = 1.4%
5%....(0.95)^104 = 0.5%
6%....(0.94)^104 = 0.2%
7%....(0.93)^104 = 0.05%
For the entire antibody test with 251 subjects...
3%....(0.97)^251 = 0.05%
4%....(0.96)^251 = 0.004%
5%....(0.95)^251 = 0.0003%
6%....(0.94)^251 = 0.00002%
7%....(0.93)^251 = 0.000001%
A series of studies find a background rate of XMRV that is all within the limits of tolerance of a varying background rate of 2-7%.
Another series of studies all find none at all anywhere. These negative studies include some prostate cancer studies.
Possibilities (ordered by most to least likely IMO):-
1. Subtleties of the blood-draw and/or testing methodology are crucial to detection; the negative studies haven't got the trick of it.
2. Cohort selection and geography are crucial; XAND and XMRV are geographically clustered (note: controls are usually taken from same area as patients so if studying a clustered epidemic this would be possible) and the CDC have been studying a different group of patients.
3. The 6 positive studies are really finding something else, an artefact of detection technique.
4. The 6 (? WPI, NIH, FDA, German prostate, 2*US prostate, ...?) studies that found XMRV are all subject to some sort of systematic contamination (unimaginable really given the consistent significant differential between patients and controls using blinded samples).
By far the most likely is the first option, indeed further unpublished and leaked science seems to point in that direction, but the second could be an interesting possibility. The third is just feasible, and could become a complex question, if the XMRV genome is variable in a complex way - there could be lots of strains and some of them "aren't really XMRV as such", for example, but other MLVs, for example. The 4th just seems ridiculous and unfeasible, even if there were contamination of certain cell culture lines, it doesn't make sense...and seems to be the preferred option of Bad Scientits at the moment so far as I can tell, along with "they're all just making this up" (which didn't seem worthy of inclusion on my list above).
Although the idea that XMRV could not swim was ludicrous, the idea that it could be highly clustered is not; some RVs are known to be geographically clustered. What makes this interesting is the idea, recently mooted here, that XMRV might only be infectious/contagious for a limited time after infection. Such a virus might spread rapidly and infect multiple people over a short space of time and then become dormant re: infectivity, and even potentially dormant re: causing symptoms, for decades or even generations. This whole scenario is interesting because of the isolated epidemics notable in the history of CFS - this sort of story does seem to have some consistency with what little is known about the epidemiology of CFS.
Perhaps worryingly, if the CDC are able to maintain that "their" CFS contains no XMRV and we have been talking about different conditions all along, then that may become a fall-back position that is being attempted for the medium term: "their" CFS didn't have XMRV and they still could be psychosomatic. Or of course they might have YMRV, ZMRV,....