The whole concept of having a publication as an undergrad as always advantageous is dumb since most people's names are only tacked on if their PI is nice and happened to publish while they were there. If you had an independent research project published, then yes that is impressive and should be a meaningful addition to your resume. Otherwise, you probably did nothing different than most undergrads with a year or two of research under their belt.
That's not really true. Being published will always look better than not being published. That doesn't mean being published makes you look better than everyone else that has not been published, but it can only help you, and let's not pretend that it doesn't.
Certainly whether an applicant is included in the author list is often up to the PI, however more often than not PI's will reward students that have made lasting, meaningful contributions over those that have done nothing. Perhaps it doesn't mean much if your publication resulted after one summer of research, but applicants putting a full year of research (including summer) and more that also have publications is typically a strong statement of their commitment and contributions to the project.
why do people still think this? look, if you actually put up enough contribution, such as setting up the system for the entire set of experiments to go through, then you can't NOT be put on the paper. it's not just that the PI decides, oh yeah, let's stick you on there. that's the reason a publication even to a medium level journal is so rare.
This isn't really true either. Tons of undergrads bust their butts but often research and publications is a political game as well. There's more that goes into who gets published than just how hard everyone worked, but that's not to say that how hard someone works isn't a component of whether or not they get published.
Sometimes the undergrad is working on a project that ultimately won't be publishable by
anyone. Sometimes the undergrad ends up being switched to a different project part way through their research tenure and thus never develop much ownership of either project.
All of this aside, I think it's important to distinguish between
undegrads that have published, and premeds in general that have. A lot of premeds have graduated from undergraduate school and gone on to research full time as a tech or other position (or perhaps even graduate school). It's likely that these people will be published, and it's important to remember that their research performance will be looked at differently than someone coming straight out of college.