By miner has to pay it, we mean "not paid to miner but to rollover pool instead"? They miner is never paying anything, they are simply not given the reward, yes?
No, by "miner has to pay it", we mean he
always has to pay it, even if he receives no on-chain fees.
You're both correct, it's a matter of terminology.
The miner has to pay it. But he's not paying by spending any of his previous coins, he's paying by having the payment deducted from the reward he collects. If the reward is not sufficient (negative reward after deduction), the block is invalid.
So the miner will not include so many transactions that the penalty will make the block invalid.
See my previous comment and I hope everything is clearer now. I apologize for not intervening sooner, I had a busy day, maybe this whole exchange could have been avoided...