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I agree those are misuse. For the first one, the network cannot be the actual creators of the work, especially as a creator adoring their own work (even one they only co-wrote) isn't really noteworthy to begin with. As you say, it would be the people hosting the fic on their site, if anything, who'd count as the "network".
For the second example, I can see how the person who wrote the example might think that this idea counts, because a beta reader's role can be considered the fanfiction equivalent to a copy editor's in published works. But as you say, a beta reader has no legal or professional leverage over the author's creative vision, and is essentially just someone giving feedback to the author (even if the feedback is pushy, as in this case.) So calling them an executive is too much of a stretch.
There are, I think, cases where I can imagine Executive Meddling applying to fanworks, because all it really needs is for one person involved with making a work to have more power than others. But pushy reviewers certainly doesn't count. I suspect that subpage has sufficient misuse that it probably just should be cut.

Now, I know that the word "Creator" can mean more than just "the person who came up with the idea" and can include others such as actors. Can something similar happen with the words "Network" and "Executive"? Because it looks like some example think so.
For example, Trivia.Infinity Train Seeker Of Crocus has the trope Adored by the Network listed even though it is a fanfiction. So in this case the word "Network" does not refer to a traditional broadcasting company, but to the writers of the work. Trivia.A Thing Of Vikings includes the trope Executive Meddling, although it is also a fanfiction, so it uses the word "Executive", not to refer to the people on the administrative side of the project, but to the reviewers of the work (I would like to add that the author apparently ignored their meddling). This last trope even has a page dedicated to Fan Works
This all seems like a stretch, since fanfiction is self-published, so the author has absolute power over the work. In any case, the closest thing to a "Network" and "Executives" would be the mods and the people who run Archive of Our Own, the website where these works are made public.
Edited by SoyValdo7