As far as I understand, the claim is actually that an Alpha particle is made up of quarks and gluons, the same number you would find in 2 protons and 2 neutrons, but that the proton and neutron are different things.
It sounds like there's a very technical distinction about exactly how you define a particle. Essentially, I believe that the claim is something like saying that modeling an alpha particle as 2 neutrons and 2 protons loses some information that you would have if you model it as 12 quarks, because the 12 quarks interact in (slightly) different ways than a proton and a neutron would.
But that sounds like a difference between two models, not a difference between two physical objects. To me it seems that if you were to follow this line of thinking religiously, you could then never say things like "an atom of carbon has six protons", since, well, they're not quite protons according to this logic.
It sounds like there's a very technical distinction about exactly how you define a particle. Essentially, I believe that the claim is something like saying that modeling an alpha particle as 2 neutrons and 2 protons loses some information that you would have if you model it as 12 quarks, because the 12 quarks interact in (slightly) different ways than a proton and a neutron would.