See if it absorbs water, especially the dark spots. If you think about it all you are doing is giving something for your primer to soak into. If you put it down over something smooth and non-absorbent, it will peel up. Spill some water on the floor then wipe your hand across it. It should soak up quick and look almost dry.
No expert, but I was in your shoes and ended up renting two grinders. In hindsight a little touch up with a hand grinder in a few areas would have probably done it for me.
-Clint