Uncertainty in measurement and total error - are they so incompatible?

There appears to be a growing debate with regard to the use of "Westgard style" total error and "GUM style" uncertainty in measurement. Some may argue that the two approaches are irreconcilable. The recent appearance of an article "Quality goals at the crossroads: growing, going, or gone" on the well-regarded Westgard Internet site requires some comment. In particular, a number of assertions which relate to ISO 15189 and uncertainty in measurement appear misleading. An alternate view of the key issues raised by Westergard may serve to guide and enlighten others who may accept such statements at face value.