Are you sure oil is leaking from the line and not merely dripping steadily onto the line from some other source? If the line in question runs from the transmission to its cooler it will be filled with transmission fluid, not oil. The former usually looks, feels and smells quite different from engine oil. (The insulation may be as much to prevent damage from chafing or other contact as for heat control.)

Wild but experienced guess: Oil leak on the right side of a six-year-old BMW I6 fairly screams "valve cover gasket." If it is indeed oil, follow that line and look for leaks above it along its entire length. You may have had a steady drip onto the foam for some time that eventually saturated it through capillary action.

__________________
2011 335xi Individual 6MT - Azurite Black Metallic / Oyster & Black / Anthracite Maple + all the good stuff
 
N47° 35' 30.13" E11° 10' 33.36" - End of break-in period. You can guess the rest. BMW CCA