It is if you're measuring the two quantities at the same place-- "work" has no other definition. For all I know the tangent-to-the-curve rule works out best in practice, with jet airliners, but it wouldn't necessarily apply with some other kind of engine.
After all, a 747 burns what, maybe 11-12 kg/km in the cruise? Does a tug burn that much, towing the same-weight 747 on level pavement?
Minimizing drag assumes that the only losses are drag based which is not true. The differences are determined by the type of powerplant that is used, be it thrust or power limited. Thrust required (drag) trends with the square of the velocity, but power trends with the cube of velocity. That is why you don't want to fly a thrust limited system at maximum lift/drag (unless MDD is slower than L/D for best range), i.e., min drag (this maximizes endurance but not range). Ideally, with a perfectly ideal jet aircraft and no Mach limit you will fly it at a constant dynamic pressure and a L/D of 0.866 L/Dmax. The reason for doing this is that this is the maximum on the thrust/velocity/range surface.
The tug is power limited, just like prop drive systems are, this indicates that range would be maximized at the minimum drag point. This would not, however, maximize endurance.
Fuel burn is a direct relation to work performed and entropy losses, i.e., system power/efficiency. In powerplants the standard way of measuring fuel consumption is via time. TSFC of PSCF. to move from time to distance you need a velocity.