No, that is not what people are saying. What they are saying is that there is information in the initial state of a system that is lost when you make a measurement. If you have an electron that is in a superposition ##\alpha |u\rangle + \beta |d\rangle##, there is information in the coefficients ##\alpha## and ##\beta## which is (apparently) lost forever if you measure the spin.I totally agree.
Let me state the other (ie, wrong) logic explicitly and as I understand it:
They are saying that before the measurement or collapse, there are many possible outcomes. But once the measurement is made, there is only one. They believe this could indicate a loss of information.
@Stephen Tashi is right, that there can also be a gain of information in a measurement, but it isn't always the case. The paradigm case of gaining information is an entangled electron-positron pair. There is only one way to produce a spin-zero combination, so the information content of the entangled state is zero. But when you measure the spin of the electron (say), you get a bit of information, either spin-up or spin-down. So the information afterwards is more than beforehand.
The talk about unitary though is all about loss of information about the past.