Despite the fact that I believe that certain people have made statements that are perhaps best termed less than forthright, I wanted to make some comments about this issue.
As is likely true, much if not most of the nearded dragon stock in this country has come from small group(s) of imports. There has been so much "cross-pollination" of breeders that it is likely that adenovirus has passed through or resides in the collections of most if not all major breeders. If that is the case where is the epidemic of deaths?
The information that has been posted, while no doubt relevant, is opinion, and is based on anecdotal experience (I have seen...) and is not based on prospective peer reviewed studies.
There are multiple serotypes, or strains, of adenoviruses. Some are probably more likely to be pathogenic in bearded dragons than are others, but no one has done the studies to find out which ones those are. Think about E. coli and the recent outbreak. We ALL have E.coli in our large intestines, jut not those particular strains that cause disease.
A negative test does not prove negativity. Even if the test could absolutely rule out virus in the feces (which it does not do completely as there are admittedly false negatives) that only proves that there was no virus being shed at that time. Think about having a cold sore, a herpes simplex virus infection. Those are persistent infections that are sometimes active and sometimes inactive (BTW some people with cold sores develop life threatening herpes encephalitis too). One is not shedding herpes virus every day so one negative test is not conclusive. Neither is one negative fecal for adenovirus. In fact, we don't know how often an infected, asymptomatic animal sheds virus as those studies have yet to be done.
Another analogy is the bacteria N. meningiditis, the causative agent in meningococcal meningitis. It may be present in 1-2% of "healthy" people's oro-nasopharynx up to perhaps 20% of people living in crowded conditions such as prisons, army boot camps, and college dormitories, but very few go on to have disease. This bacteria is a killer once it causes disease, but does so in very few people who carry it.
So...what are people to do with all of this? I don't know. For people who have had several animals die from this, well they were probably infected with a more pathogenic serotype or had dragons with some other immune system problem. That's a guess but until there is actual data, which may never come, it is a reasonable one.
For the rest of you...well I have some dragons that I'm not planning to breed and I'm not going to test them. But if I were going to breed them I'm not sure that I would because I'm not convinced that I have enough information to know what to do with the results of the test, especially if they are negative. I would have a hard time saying my dragons are truly negative with one or even two negative tests. And even if they are positive, they are thriving and appear quite unaffected. Until you know what to do with the answers, asking the question only leaves you with more questions.
The scientific studies need to be done, for sure. But don't expect that to happen anytime soon as they cost lots of money to do. Until then, it's Russian Roulette no matter what choice a breeder makes. But I, myself, with my scientific background, would not take one negative fecal as "proof" of an uninfected colony by any breeder.