My optimistic interpretation is this:
You have 4 rolls per week: 1 roll for Mythic, 1 for Heroic, 1 for Normal, and 1 for LFR.
If you kill Sarkareth on Mythic (first), then you get all four rolls: Mythic, Normal, Heroic, and LFR.
If you kill Sarkareth on Normal first, then you roll for Normal (at the Normal%) and LFR (at the LFR%), and killing Sarkareth on LFR will not get you another roll (so there is no reason to queue for LFR Sarkareth, as you’ve already used your LFR Sarkareth roll).
However, having killed Sarkareth on Normal, if you then kill Sarkareth on Heroic, you get one more roll on the Heroic % chance.
I have no idea whether this interpretation is correct, but to me it seems the closest to what Blizzard was trying to say. Further clarification would be greatly appreciated.