Right, "the people who are concerned about this sort of thing" and push that agenda on the wiki page. Next to misconceptions like Columbus proving the world was round and that the daddy-longlegs is the deadliest spider, arguments about about how precisely to simplify elementary education of the scientific method are rather out of place.
Seriously, is it worth piling on concepts like peer review and publication to education of the scientific method? Peer review and publication are specific contemporary terms used by professional scientists. If you're a regular person and want to learn something, for example, how a particular feature of a programming library works, or how much load your servers can handle, or how spellcasting works in your favorite MMO, it's far more useful to understand the so-called 'rigid' scientific method than it is to understand peer review and scientific journals. It's not a "misconception."
I would say it's important, although the base is of course also important by itself.
People in general rarely understand how science really works. It's glaring in journalism where often an article takes some non-reviewed research and cites it like it's an established truth, or in vague quotes like "some scientists believe X", where the scientist is actually in a domain not at all related to X. I also see a lot of people who cannot grasp how a given source may be more reliable than another one, even if both are written by "scientists". Things like the "evolution is just a theory" would also be less prevalent if people understood how science works.
Journalists don't write articles like that, though, because they are thinking in terms of the textbook definition of science. They write like that when they have less interest in knowledge and intellectual rigor than emotions and gossip, in which case the meaning of science is not important one way or the other.
Comments like "evolution is just a theory" would be less prevalent no matter which definition of science was applied: the simple, elegant textbook definition or the complicated, several-page Berkeley definition. The problem is not that one is applied over the other, the problem is that neither is applied..
Seriously, is it worth piling on concepts like peer review and publication to education of the scientific method? Peer review and publication are specific contemporary terms used by professional scientists. If you're a regular person and want to learn something, for example, how a particular feature of a programming library works, or how much load your servers can handle, or how spellcasting works in your favorite MMO, it's far more useful to understand the so-called 'rigid' scientific method than it is to understand peer review and scientific journals. It's not a "misconception."