The guidance does have a defintion of ownership: "Under § 61, all gains or undeniable accessions to wealth, clearly realized, over which a taxpayer has complete dominion, are included in gross income."

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.