I would say this advice is in general not true. EC's are very important when applying to residency, just in a different way than how EC's were viewed when applying to medical school.
On your application to residency, the EC's are split into 3 broad categories of research (can keep undergrad research on there too), work experience (anything paid, clinical experiences, or teaching experiences), and volunteering (volunteering in the traditional sense + everything else that is not research or work). Given that the only parts of your entire application you work on are your personal statement, the EC section, and your hobbies, I would highly NOT recommend applying without EC's. The rest of your application (test scores, letters, transcript and school performance) are basically done and/or out of your control (letters) by the time you apply.
How are EC's viewed and how should you approach this?
- Do things you love and feel passionate about. Even if they are informal, as long as it's something important to you and you've done meaningful work with it (I don't know like if you play the organ in your neighborhood church every Sunday - sorry for the random example), you can put it on there. These are good conversation starters for interviews - "Oh I see that you've been playing the organ for years - tell me how did that start? Have you always played an instrument?"
- Try out things you think you might be interested in, even if it eventually doesn't go anywhere. Research doesn't have to be super hard core in med school. Find a case report, do some chart review, just show that you can do scholarly work. Publications are great but they're not everything (unless you are applying to ortho/ophtho/derm/plastics/ultra competitive specialty). As long as you can have an intelligent conversation about what you did and what you learned from it, it can be a great EC.
- Do things that demonstrate some desirable characteristics. Once again, can be in anything. You can join your med school student government - show leadership skills. Become an organizer/leader in your volunteering work. Mentor and teach other medical students. Coach a youth sports group in the summer. Leverage your skills! If you love gift wrapping, maybe you organize a group of med students and offer to help wrap gifts and donate them - the world is your oyster!
At the end of the day though, your academic work must come first, so don't sacrifice your grades and test scores for EC's. But if your scores end up not being the most amazing scores there ever were, then having an impressive list of EC's will be very important in helping you gain that coveted residency position. With step 1 now P/F and some schools having P/F rotations too, I suspect EC's will only become more important as time goes on.