A few data points and references. I don't think anything is fishy, I believe we are trying to use NACp in a way that it was not intended.
The accuracy defined by NACp is very course, and is intended to aid ATC in their typical 3 and 5 mile separation of IFR traffic. Not necessarily for precision or close range collision avoidance.. The ATC "system" (generic sense) relies on both GPS integrity and accuracy.
NACp is derived from the instantaneous accuracy figures, but is conservative number to indicate "95% accuracy limits for the horizontal position that is being currently broadcast" (from DO-260B). Therefore, the number represents a 95% certainty that the "target" is within that circle. Even if the instantaneous calculation is fairly accurate, there may be conditions (constellation, lack of SBAS, atmospheric, airframe shadowing) that cause the 95% certainty "bubble" to expand.
Also from the same doc: NACp "is reported so that surveillance applications may determine whether the reported geometric position has an acceptable level of accuracy for the intended use. Note, none of these uses indicate GA self separation.
As for the intended use, the table below for reference, also from 260B:
I know of no other EFB that uses this figure in this way, but I could be wrong.
Also, I know its been discussed before but integrity and accuracy are different things. An interesting discussion can be found here:https://gssc.esa.int/navipedia/index.php/Integrity#Integrity_vs._Accuracy
Finally, an interesting article, while not exactly relevant to the discussion - can give some insight into the various space and atmospheric conditions that can degrade GPS performance at any given time.https://www.gpsworld.com/the-iono-blob-holds-back-air-safety-advances/