I am fine with the narrower definition, simply because I don't believe there is a significant difference between them. I already accept that there are some differences between brains and AGI that can be ignored; e.g. I don't think an organic substrate of neurons is necessary. But this is not the spectrum along which the argument is usually being made.

Implicit in the argument that "bare" cognitive tasks may be performed different from how they function in the human brain is that one can optimize on how the human brain performs cognitive functions by not requiring a perfect mirror to biology. Otherwise, why would you care about the difference? Either an AGI is the same as the human brain along a particular feature/ability, or it is better, or it is worse. If worse then it doesn't feel like true AGI. If the same, then the difference is irrelevant. I think your argument is that it could be better. This, I think, is where there is a frequent misunderstanding. Although it is true in many respects (e.g. I wouldn't want to create an AGI with Alzheimer's), more often what people deem to be weaknesses in natural brains are actually strengths.

For example, a selective memory that focuses on what is important to the agent is not just a space-saving efficiency, but also makes the process of finding the "right" answer easier, since there is no clutter to lead it astray. When planning, I'd like the options available to me to only be the best ones, the ones that directly benefit me, and to remove those that could possibly be harmful, and I prefer that arrangement at the expense of a diversity of options. This narrowness of thinking may be seen as a weakness, but is actually a strength - especially in a dangerous, resource constrained environment (i.e. our world). This is just one example, but it makes the more general point.

Hope that clarifies my perspective.