Drugs testing was not particularly effective 10 years ago, for instance in 1999 there was no test for EPO, and we /still/ cannot detect all forms of blood doping. There is a disputed positive test for EPO from Armstrongs blood (the dispute is about whether it was stored properly etc. the test was not contemporary to the racing). We also know that cheating was very widespread. (see this wikipedia page: http://en.wikipedia.org/wiki/List_of_doping_cases_in_cycling#2000 )
The effectiveness of EPO and blood doping at boosting performance is sufficient that it is unreasonable for someone to consistently win against cheaters in the way Armstrong did. The leading racers today output around 10% less power (for the same weight) than Armstrong consistently managed, in spite of advances in training technology. We also know that the peloton rides substantially slower now than it did then, further indicating that cheating was the norm. Many cyclists have reported that the widespread nature of doping was an open secret among the riders. David Millar reports that team directors routinely used euphemism to tell their riders to dope, and that he was told by his to "Go to Italy and train properly".
Armstrong was consistently able to ride away from that doped-up peloton on climbs. This does not seem feasible.
Armstrong's team was also able to dominate that peloton consistently, and many of them have been implicated in/ banned for drug taking, and have also accused Armstrong of it. Added to which, Armstrong has had doctors of his be subsequently banned for organising and carrying out doping.
When you consider how dominant Armstrong was, how much doping was going on among his competitors, the extent to which those people working with him have been found out as cheats, I'm not sure it is possible to maintain that it is more likely that he achieved all of that clean than that he managed to carefully plan his drug taking to (almost) avoid being caught.
The 1999 samples from Armstrong tested positive for EPO, however the tests are disputed by Armstrong. (source: http://velocitynation.com/content/interviews/2009/michael-ashenden )