You have this backwards. To a distant observer, light going into a black hole is red-shifted, not blue-shifted. If this were not the case, sending even a single photon into a black hole would produce infinite energy.
No, any photons that are emitted from matter close to the event horizon and travel toward the distant observer will be redshifted. Photons falling into the potential well of the black hole will be blueshifted. Of course, the distant observer is not able to directly detect photons falling into the black hole because he is far away from it. All he can do is calculate what he would expect the energy of the photons to be. This calculation gives an infinite energy as the photon approaches the event horizon, but it's not a "real" energy, so the black hole doesn't gain an infinite amount of energy.
An analogous effect occurs for an observer stationed at rest, hovering above the event horizon. Such an observer will observe the photons from afar to be blueshifed in agreement with the distant observer. Moreover, as this stationary observer gets closer and closer to the event horizon, the photons will be blueshifted to infinitely large energies.
An analogous effect occurs for an observer stationed at rest, hovering above the event horizon. Such an observer will observe the photons from afar to be blueshifed in agreement with the distant observer. Moreover, as this stationary observer gets closer and closer to the event horizon, the photons will be blueshifted to infinitely large energies.