What's wrong with this is that material doesn't fall straight in to the black hole, but whips around in a tight orbit--the accretion disk--so that the radiation from the infalling matter is successively redshifted or blueshifted by the Doppler effect, depending whether it is travelling away from you or towards you.
pings for good FReepers!
The part that you quoted isn't over your head. You know that when a police car or ambulance is coming towards you, the pitch of its siren is higher than when it's travelling away. That's the Doppler effect. It is most pronounced when such a banshee passes you; the change in pitch is familiar to everyone.
If a police car were travelling in a circle some distance away from you, you'd hear the pitch of the siren going up and down, up and down as the car travelled around the circle.
Well, the frequency of light is nothing more than its pitch. Blue frequencies have a higher pitch than red frequencies; ultraviolet light has an even higher pitch, and x-rays have a higher pitch still. So, naively, we'd expect the light emitted from infalling matter to go up and down repeatedly in frequency--just like the police siren--as it travels around the black hole. But that's not exactly what's seen.