I don't think the comic is saying that that's wrong per se, but it can be be very problematic to say the least.
The comic frames this as a situation where the problem is "too few stories about X group" with the implied understanding that there is also a related problem of "too few stories told by X group". What the over-represented Y group does in telling stories about X group addresses the "about" problem, which is good -- diverse representation in both fiction and non-fiction is absolutely a good thing, especially when it's founded on good research and a genuine desire to empathize. But it also does nothing to address the "told by" problem, because Y is still an over-represented creator group (never mind the problems that arise when a lot of members of Y group don't do their research or muddy their presentation due to lack of experience/sensitivity). Whatever stories being told may be important, yes, but when you still have an issue of living, breathing creators from marginalized groups who aren't being heard or paid to tell their stories nearly as often as the dominant group? It kind of undermines the idea that those groups are actually being supported.
I think you answered your own question on this one, though: input from members of the group is key to working against both the "about" and "told by" problems. Ideally, when telling stories about a marginalized group while also being a part of a dominant group, members of the marginalized group in question should get to be key voices in the creation of the work and have a chance to tell at least part of the story in their own way, and to be credited and paid for their work.
At the very least, though, if you take input or consultation from marginalized people without having them on as a part of the main creative team, you then should make sure you do your damnedest to also amplify things that marginalized creators do make. Put a platform somewhere in your work and in the promotion of said work to direct people towards more creations and causes of the people you're advocating for. Link to creators' crowdfunding campaigns or Amazon listings, tell your followers to check out their stuff online, donate to fund more of their works, invite them to collab with you on future projects, etc. Basically: signal boost awesome creators like crazy!
Your work may always have a problematic side to it by virtue of it continuing to boost the already over-boosted white creator market (heck, that's a problem I acknowledge in my work too), but that doesn't mean you're not allowed to create or tell the stories that inspire you, especially not if you're putting in your due diligence. As long as you're not the cat who performs those stories without actually acknowledging that toads can tell stories too, then you'll go a long way to help counteract the problem.