Theranos was at the right time with a very intriguing idea, but one that was ultimately not a model for reality. They were able to get lots of capital at this time in preparation to develop a product that ultimately never materialized (and more fundamentally, may not be physically possible).
http://www.cbc.ca/news/canada/british-columbia/uvic-blood-te...
To be honest, I don't know. I think it is possible to get a lot of information out of a single drop of blood. But there are issues with sampling--blood from the capillaries in my finger is very different from blood coming back from my intestine.
Maybe more fundamentally: a lot of "interesting" things are specific proteins. These can be at extremely low concentration--on the order of nanomolar all the way down to femtomolar. It's very difficult to amplify such a signal -- DNA is easy to amplify but proteins are not. At such low levels, the wrong drop of blood may have a dramatically different meaning, due to stochastic effects.
More likely I think they were also enamored with what looked like promising results. I've personally seen situations where technical due diligence on lab tech was poorly done and therefore wrong. Unless the VC has a fairly strong science background/scientific advisors in a related sector, it's super easy to make something look like it's working when it's actually totally busted.