RNP is the design requirements of a procedure and does not change.
ANP is the ability of an FMC to project accurately the desired course. The confidence that the FMC has that it is accurately projecting the course is measured in NM. This is measured as a CIRCLE with a 95% confidence that the aircraft true position is inside that circle. The reason it is not a sphere is that most aircraft flying these approaches are using Baro VNAV for vertical projection which in not subject to a Vertical ANP. Vert ANP is coming but it is not here yet as it does not use Baro-altimetery.
Crosstrack Error and Vertical Deviation are the aircrafts ability to fly the FMC projection.
What they are actually saying is that using WAAS the FMC has a capability of very low ANP. The press and most line pilots usually gets ANP and RNP mixed up because of a lack of understanding.
At present the B737 NG have the lowest RNP demonstrated values for jet transports of 0.10 which in a low threat terrain RNP AR approach is close to 250 feet AGL DA. With WAAS or GBAS a lower RNP may be able to be flight demonstated, this should allow an aircraft with a low ANP ability to fly a low (below 0.10) RNP approach. The world of RNP is moving fast so the G650 and other new designs may be able to achieve lower soon.
Note the bold, we use that in our airline to describe the three components that make up Performance Based Navigation;
Design, Project, Fly = RNP, ANP and Crosstrack Error + Vert DEV