What's the advantage of using non-truncated mining targets? Bitcoin Wiki (Difficulty):


  The highest possible target (difficulty 1) is defined as 0x1d00ffff,
  which gives us a hex target of 

0x00000000FFFF0000000000000000000000000000000000000000000000000000

  
  It should be noted that pooled mining often uses non-truncated
  targets, which puts "pool difficulty 1" at

0x00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF



From what I know, using non-truncated targets puts the target at a higher number than the network would accept. In other words, we may end up finding a hash accepted by the "pooled mining" (lower than non-truncated), yet rejected by the network (higher than truncated).

Why do people use non-truncated mining targets?

Why not simply use the actual truncated targets so that we can have a more accurate picture of the network and avoid overheads incurred as such?
You are right, it could happen you are finding a hash that meets the pool target but not the highest possible target. But because the difficulty is way higher than one, and therefore the share wouldnt finish the block anyway, its not in their interest. You have done your work and you will get your share. They just make it a bit easier for you, by passing a higher target than possible.

Another possible reason:
Comparing a hash to the highest possible target would take more time, because you have to check the whole hash (checking the zeros at the end as well). With the non-truncated target you only need to check until the first F occures because than its at least equal or lower.