Removing your corporate brand from a damaged aircraft (or car or cruise ship or any other malfunctioning, high-profile item) seems like a sensible thing to do. It will reduce the number of photos that tie your brand to an accident, and, for airlines, it probably reduces customer worries.
But painting over your logo with black paint is not the best way to go about it. Even after Thai Airways hastily applied the black paint, anyone familiar with the Thai livery could instantly recognize it from other colors. This is the irony of a good brand. When it is well done, people recognize your product from incidental fuselage and wing markings, body colors, the logo shape, or some other small design detail.
If you want to do it right, you must remove all brand elements. It is much better to cover everything with white paint, so that the aircraft just looks unpainted, not just partially covered up. Alitalia demonstrated this earlier this year when one of their ATRs skidded off the runway in a similar incident. Note how all the recognizable colors were removed, not just the logo: