I have two different programs for "integrated elsets" and two different ways of using one of the programs.
1) The program "int2" is used for most "high" objects. Int2 is not strictly speaking a numerical integration program. It is a program which is capable of adjusting the orbital elements according to its model of drag and a few 12-hour resonant terms of the Earth's gravitational field. In general, int2 will keep the mean motion constant unless it is computing a non-zero drag term.
It is somewhat compatible with SDP4 in many cases, but users should be aware that any object like Mentor 2 which has a mean motion near 1.0027 is assumed to be maintaining a constant longitude. So in that case it is not compatible with SDP4 since SDP4 is not capable of assuming that an object is maintaining a constant longitude.
2) Most of the objects which have a mean motion of 1.0027 also use "int2" in a special way which is supposed to maintain the constant longitude more accurately than pure "int2".
The "int2" program also computes the effects of solar and lunar perturbations on the inclination, node, and eccentricity. This is appropriate for most of the classified objects since most of those objects are not trying to maintain a near-zero inclination.
3) The objects which have a mean motion greater than 0.9 or so and an eccentricity near zero (and are not trying to maintain a constant longitude) are maintained using the "int3" program. This is a true numerical integration program. It has a number of terms for the Earth's gravitational field, but the important ones are the 12 and 24 hour resonant terms. It also has solar and lunar perturbations.
The mean motion at the epoch of the last observation (which is what is found in classfd.tle) is not truly compatible with SDP4 because the mean motion usually differs from the "adjusted" mean motion that SDP4 computes and uses.
The elsets produced by int2 and int3 in the "integrated" elsets file (inttles.tle) are reasonably compatible with SDP4 at the current epoch because the time difference between the epoch of the elset and the time of prediction should be very small.