That statement isn't a put-down of songs or songwriters. It's a simple recognition that as a songwriter or performer, you are making music. And that means that musical skill matters, no matter what your specific goals might be.
Notice that I said "skill" and not "ability". We need to sidestep the talent question here. There's no question that we here in Nashville are surrounded by some of the most naturally gifted people on the planet, and some of their ability comes from that natural gift. But I'm referring to the kind of skills that can be developed through conscious effort (and the willingness to put that effort in).
A songwriter can find any number of resources on writing better lyrics. We look at form and meter. We can learn to use a thesaurus and rhyming dictionary, and always aim for the best way to express an idea. Since we all use language, we know different ways we can say the same thing. That gives us options to choose from, which absolutely helps elevate the craft. But when it comes to music, it seems like many people learn the most basic (read: limited) vocabulary they can get away with and stop there.
Now, let's be clear: I'm not making an argument against simplicity. But there's a difference between simplicity as a conscious choice vs simplicity as a lack of alternatives. I don't think anyone would argue that an adult with a first-grade vocabulary might be limited by that simplicity. In any verbal or written communication, we want to be understood and choose our words accordingly. The larger your vocabulary, the more ability you have to communicate in different situations. So the same goes for music. If you've learned six chords and two strum patterns and stopped there, you haven't finished elementary school and will likely find yourself in situations where you can't communicate effectively.
I think a lot of people have a fundamental misconception of what musical skill means. We watch accomplished musicians and might think, I'll never do that, or I have no interest in doing that. But what you don't see (or hear) is actually more essential than the notes you hear in a performance. Real musical skill has to do with choices and options: knowing that using this chord instead of that one will give a word or a line more (or different) emotional impact. Understanding that groove - the element of music that literally makes us move - comes from how we feel the music, not just from how you swing your arm to strum a guitar. Knowing how to work with a melody when your voice can't hit the notes or your fingers can't negotiate the keyboard.
All of these things are ultimately very simple, and come from a base of knowledge and concrete skills and tools that anyone can develop. Yes, the ability to perform any act well takes effort and dedicated practice. But you might be surprised how much you can accomplish with just a little. Then again, you might not be...three chords and the truth, right? The question is, which three chords?
My primary point is that you can learn to play your songs with more command and authority when you have an understanding of what you're doing. Otherwise, you're just executing a series of movements somewhat blindly. You can write with more freedom and flexibility when you have a bigger vocabulary. The naturally gifted intuitively grasp this, but may not be able to explain it. The good news for the rest of us is that it CAN be explained in a straightforward way, and in a way that can make an immediate impact on your writing and playing. But you need to recognize two things first: one, that you're capable of doing more than you can today, and two, that you would benefit from that growth. In other words, it starts with your mindset...the rest flows naturally from there.