If you are the sole possessor of a private key which grants control of a cryptocurrency address then you have complete dominion over the crypto at that address. Under situation 2 of the guidance: "B has dominion and control of Crypto S at the time of the airdrop, when it is recorded on the distributed ledger, because B immediately has the ability to dispose of Crypto S."
Taken in the most taxpayer hostile interpretation that means that if the ledger is duplicated you have income because you have the ability to dispose of the forked coin with your private key even if you have no desire to touch it in any way.
As an analogy: if I get paid by check on december 30th, and the check doesn't clear until january 2nd, is the income for the old year, or the new year? What if I hold onto the check, waiting for the new year? How about if I have the check, but I'm snowed in, and can't get to the bank? What if I can get to the bank on december 30th, but the bank is snowed in and closed?
(Answers: old year, old year, and then two don't knows)
> even if you have no desire to touch it in any way.
Not just desire, in most cases people don't even know about most of the cryptocurrency forks!