Yes, it does not sounds a scientific speech but it has sense:)
You can think that the polarizer is some "observation", "measurement", that makes the particle occupy one of the eigenstates.
For the first polarizer, the allowed states were up and down, vertical polarization) or left and right (horizontal polarization). Before reaching the polarizer, the photons were in mixed states, neither up and down nor left and right - arbitrary direction of polarization. Think that the polarizer can observe the polarization of the incoming photon, but observation makes the photon jump into one of the allowed states. The polarizer will "observe" an up-and-down photon and a left-and right photon with equal probability. It let's through only up-and down photons.
The second polarizer is "oblique" with respect the first one. Its direction of polarization can be 45° with the vertical, for example. The allowed states are also oblique, NW-SE and NE-SW. With respect to those states, the up-and-down photons are in mixed states. When the polarizer "observes" them, (they get into contact with the polarizer) they jump into one of the allowed eigenstates. That is meant by the sentence "Listen guys, you thought you were up & down, but that aint true. Everybody has to be oblique this way or that way" and the polarizer let's through only one kind of photons, those in the eigenstate NW-SE.
Edit: DrewD beat me, my explanation is basically the same as his.
ehild