Right, so then we're back at my initial question: Is difficulty irrelevant as long as you know the net hash and your own hash rate?
Sounds to me that it is irrelevant. I mean, the difficulty by itself doesn't mean anything if you don't know net hash and your own. But if you know the net hash and your own, the difficulty number is irrelevant.
So I'll throw another 2 Satoshis-worth into this discussion.
You're correct. Difficulty is not a direct factor. You have 10% of total, then you'll earn roughly 10% of the total payout. I say Roughly, because of the random nature of crypto-currency mining. Some miners are luckier than others in the short term. In the long term, it will mostly even out.
Depending on the rules of the particular coin, difficulty will change +/- as the total hash-rate affects the rate of production of the blocks/coins. Your portion of the total is the only thing that affects your payout.
If you had an Antminer S9, back in January of 2013, you would have been 1/2 of the total network, earning 72 blocks (* 50) or 3,600 BTC per day. That same machine today is 0.0002% of the network, and will earn you roughly 0.0044 BTC per day. Until next week, when it will earn you maybe 0.0038 BTC per day.
The difference is caused by the difficulty change since then.
Pardon me, I've got to go over some settings on my time machine...