This hypothesis does not survive comparison with even the most well known copyright cases, such as George Harrison's "My Sweet Lord", which was found to infringe on The Chiffon's "He's so fine". Also, The Verve's "Bittersweet Symphony" is literally a case of sampling the symphonic performance of The Rolling Stones "The Last Time". Someone else had already stripped away the lyrics before The Verve infringed.
Just like most court cases where the losers frame a ruling against them the worst case scenario of a problem existing on a singular axis, there are extenuating circumstances in each of these that add far more complexity to an issue than the infringers want you to believe. In the case of sampling "The Last Time", there was an agreement in place where The Verve had gone through all of the proper channels to secure the rights to use samples. However, it was ruled they used too much of the sample, as the iconic string section playing the four root notes of the melody in the song is that sample. I don't have the actual agreement to reference, but suffice to say, the ruling took into consideration that the agreement described a far more limited use of the sample, instead of looping through the entire duration of the song, which is what happened.
Then, just to wave the whole complexity of it in your face as something that is impossible to nail down to any simple rules, there are the cases in the far opposite direction that seemingly should be infringing, but for whatever reason haven't found to be, or at least are specious enough given previous litigation by the offenders.
Neil Young sings in "Borrowed Tune": "I'm singing this borrowed tune, I took from the Rolling Stones. Alone in this empty room, too wasted too write my own"
Huey Lewis successfully argued that "I want a new drug" was infringed upon by the theme to "The Ghostbusters". I don't know the order of operations in regards to his suit, but Huey Lewis also released "Do You Believe in Love?", which is strikingly similar in musical nature, AND has nearly identical lyrics to Electric Light Orchestra's "Sweet Talking Woman":
ELO: "I was searching on a one way street, I was hoping for a chance to meet..."
HL&TN: " "I was walking down a one way street. Just a lookin' for someone to meet"
Most damningly, one would think, is that at various times in each song, there are three part harmonies that echo the verb of each stanza.
For any Godel Escher Bach fans out there, the application of copyright law seems to adhere to Godel's Incompleteness Theorem.