One could use either kind of latitude to locate points on the WGS 84 ellipsoid (used by the NED) or any other ellipsoid, but "everybody knows" that the values will always be given as geodetic latitudes. However, it is surprisingly hard to find an authoritative statement to that effect!
Before we go on, it helps to understand that although a datum like the WGS 84 ellipsoid describes a reference surface to locate everything on, above, and within the Earth, it is compatible with many different ways to associate coordinates with the geometric points on that ellipsoid. Two of those ways are the geocentric and geodetic systems.
The geocentric latitude of a point is the angle it makes with the Equatorial plane.
The geodetic latitude of a point is the angle made between the Equatorial plane and a perpendicular from that point to the surface of the datum beneath it.
The two angles are the same only when the point is located over the Equator (when they equal zero) or over one of the poles (when they equal -90 or +90 degrees). Otherwise the points denoted by the same numerical values of latitude and longitude can differ by as much as several tens of kilometers in the two systems (as I recall--I haven't rechecked that figure recently).
Both types of latitude can in principle be used, even though WGS 84 is referred to as a "geodetic" datum. (Indeed, both of them, as well as a "reduced latitude," are used in the governing NIMA technical report TR8350.2, available at http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf. See p. 4-4 and section 5.2 (on Gravity Potential) et seq.)
In the recent article Using NHDPlus as the Land Base for the Noah-distributed Model (David, Maidment, et al., Transactions in GIS 2009; 13(4): 363-377) a group of GIS luminaries writes
To distinguish between a spherical and spheroidal Earth, two types of latitudes are needed: geocentric and geodetic as shown in Figure 4.
Longitudes are not affected by this difference in Earth shape because it only involves
North-South flattening. The geocentric latitude \Phi is the acute angle measured between
the equatorial plane and a line joining the center of the Earth and a point on the surface of the sphere or spheroid. The geodetic latitude \phi′ is the acute angle between the equatorial plane and a line drawn perpendicular to the tangent plane of a point on the reference sphere or spheroid. Normal map coordinates are given in longitude and geodetic latitude.
In the 2007 book Unmanned Aerial Vehicle Real-time Guidance System Via State-space Heuristic Search, Manuel Soto makes a similarly clear statement about which latitude is used by the NED (and employs similar figures to illustrate the distinction). The relevant pages (85-88) are available on Google books.