Yes, you can/need to back thru the white line in order to get better hoof dynamics, even when the sole is thin. If you don't go back thru where that line appears to be, you'll never actually move the breakover back to where the bony column needs it to be.
With thin soles, you may need to not back as far thru the "white line" at ground level at each trim - so doing less more frequently works really well.
The white line is a seam between the wall lamina and the sole that starts at the perimeter of the coffin bone, then grows down toward the ground. It stretches forward with the sole and wall as they move forward. When you back thru where it appears at ground level and then bevel the underside of the sole in the toe region at the new location, you'll find the white line behind the new location of the end of the toe. With thin soles, do NOT touch the soles behind the new toe length at all: even if they are lumpy or uneven, flaky, exfoliating just leave them that way as that horse needs every millimeter it has at that point in time. Sole depth doesn't necessarily increase evenly across it's entire surface - many times, it adds depth in the areas most critically in need of it, which can appear as thicker/lumpier areas.
You can add jiaogulan to help increase growth rate once the trim is correct.
Jan 2005, RI