That is often the case, yes. In this case, I don’t think they were protecting HIS reputation, I think they were protecting their own. Her comment was factually true, but the timing was in poor taste. He hadn’t been dead 24 hours.
As you point out, there is room to debate WHEN it is appropriate to speak negatively about someone who died tragically. I don’t know when it’s appropriate but under 24 hours seems dicey, even to me.
The instant backlash indicates that a lot of people also found it in bad taste. If the instant response had not been negative, the Washington Post would likely not have reacted the way they did. Thus, they are taking care of their reputation, not Kobe Bryant’s.