Without seeing the surface, I'd guess these spots are small pits filling with contamination.

I am having this same experience and am heartbroken. Small, dark black spots all over certain pieces of the marble. I have been researching the problem and have left a sample with a near bye quarry to see if they can come up with an answer. I have another room to do with the same marble and would like an answer before I install the next batch. Hopefully someone has an answer.

I had two small black spots show up on a Glacier White Corian refinish today. I ground 'em off.