DannyHamilton just explained that there is no universal timestamp.

And even if I went your way, it would only make the mystery much deeper: If really most empty blocks are found within a second, and we have about 1% empty blocks on average - that would mean the probability to find an empty block within 1 second is 1%. Not 1/600th of the average block time of 600s.

Do you imply that different mathematics of difficulty apply to empty blocks?
If yes, why would any miner "waste" 99% of his computing time on finding full blocks, when mining empty is so much easier?