Interstitial glucose sensors can be reasonably accurate, but there are two main concerns: the sensor response time, and calibration.
Glucose diffuses from blood into the interstitial fluid, and it can take some time during periods of glucose change (e.g. after a meal) for an equilibrium to be reached. Hence, the sensor measurement will lag behind the true blood glucose level. The blood glucose is what people are generally interested in, so measurements of interstitial fluid are used to estimate the blood glucose level, and so are only valid during periods of stability. With careful management of sugar intake this can be an acceptable compromise however.
Most CGM sensors require calibration against a reference instrument such as a test strip-based device using a finger-prick blood sample. As long as this is done during a period when the interstitial glucose level is stable, the sensor can hold calibration for several hours and indicate the trend in the blood glucose concentration.
The Theranos product is something completely different, and isn't suitable for day-to-day monitoring of blood glucose levels. The samples are sent away to their lab, so there is a delay in receiving results. They will measure your blood glucose level but this would generally be a fasting measurement to provide a background level. Nevertheless, this (should be) a more accurate test, as it is laboratory based and takes a physical blood sample.
CGM sensors have been shown to be accurate to within clinically useful ranges, when used with the above considerations in mind. Specificity (and sensitivity) are only really considerations when test results are compared against cut-offs to determine a positive/negative result. This paper is a good summary: