Yes, it took me some time to understand that too.  The "lever arms" are a couple of private keys drawn from a set, that gives rise to a couple of public keys, to be combined with conditions (one is the counterparty's public key, the other is an own public key arbitrarily chosen of which one has the private key), giving rise to two P2SH hashes.  One only needs to test on average a set of 2^80 private keys to find such a couple that has identical such P2SH hashes.
Note that it is somewhat more involved than just testing 2^80 private keys ; one needs to store somehow these results to find out what couple has a collision after the fact.