The minimum difficulty required for a block to be valid is the thing that stays the same. Within that 2016-block window the actual difficulty of various blocks varies above that threshold.
It would be less ambiguous if you said, "Successful pools do not build on the first block they hear; they build on the block with the highest work they hear."
Well, we're splitting hairs here, but technically I might have gotten lucky and not worked very hard to find a block whose hash, in binary, ends with 250 zeroes in a row (outrageously high difficulty).
But yeah we're talking about the same thing.
This is a statistical fallacy. Two blocks will always be equally difficult when they were mined with the same target.
What you mean to say is that clients prefer to choose the block with the least block hash. This is effectively a deterministic pseudo-random algorithm for choosing which block to build on. I do not remember this being the case, but it is possible this has changed recently.