I think "Cooper E80" loading stems from description in the old American Railway Engineering Association (A.R.E.A) manual of practice. While I guess the assumptions may have been changed from subsequent editions or local codes/practice, I believe this procedure traditionally used Newmark's integration of the Boussinesq formula (unlike the Holl's integration used in some other truck/live loading procedures for buried pipe). This procedure assumed that the surface loading is uniformly applied (I guess in effect by the tie mat below the rails) on a surface loading rectangle with dimensions 20 x 8 feet (with the 8 feet of course being assumed effective length of ties etc., and I believe the 20 being an approximate spacing of the drive locomotive wheels/axles). At least for an early "Cooper E80" loading, I had always been under the impression this rectangle was in turn basically loaded every five feet with an 80,000 pound axle load, applying in effect a uniform surface load of 2,000 psf (13.9 psi) on such rectangle.
I cannot tell you exactly what the specifier means without further information by the "2,600 lb/ft" you state, nor for that matter how it necessarily relates to design for all conceivable effects on any "liner"; however, I believe that number is probably quite close to a sum of the level of live loading pressure you say is applicable at pipe depth (I guess from such integration) plus earth load pressure at pipe depth, converted to a load per foot on a 12"size pipe.