Cpt Blogs
In theory... but do you really think a system would be approved for RNP 0.3 (eg RNP Approach LNAV) if all it could do was put you within 0.3nm of the Centreline? That is "miles" off and you'd never get in on any min-vis approach. What about RNP-AR at RNP 0.1? "What are you complaining about? You're only 200m off the centreline!".
On all the GNS approaches I have done (practice VFR approaches for training), the approach is a pseudo non-precision, and not an ILS replacement. The idea is to facilitate difficult approches in high terrain. So many of them bring you in with a large approach offset, terminating in a decision of about 1,000 ft or so.
If you have a 3 nm missed approach point, there is not much point in having lateral accuracy much greater than 0.3nm. The approaches are nice, down the valleys etc. But there are gotchas, like where do you go if the FMC loses the curving path half way down.