they don't, but they also do.
set your cube up with this R U2 R' U' R U' R'
that's the inverse of the most popular sune alg, R U R' U R U2 R'.
there's other sune algs than that, which effect where the pieces will go.
if you perform R U R' U R U2 R' while the OLL is sune, the ULM edge will switch with the URM edge, which switches with the UBM edge.
the UFR will switch with the UBL corner, and the UFL corner will switch with the UBR corner.
when you perform R U R' U R U2 R',
ULM-URM-UBM CCW edge cycle
UFR-UBL corner swap, UFL-UBR corner swap
now if we set up the cube with a different algorithm(although the orientation will be the same as if you performed R U2 R' U' R U' R'), the permutation of the pieces could be different.
let's set the cube up with L' U R U' L U R'
the edges are already permuted, but 3 corners have been cycled clockwise(UBL-UBR-UFR).
with the sune orientation showing, let's use the R U R' U R U2 R' algorithm.
WAIT! the setup earlier solved the cube! it's still the sune, but it didn't solve!
well, you could've solved it with R U' L' U R' U' L.
see what i mean about the OLL effecting which PLL you can get?