Now that I have kids, I see there is at least a grain of truth in it. My oldest son, now 14, is still basically the same kid he was at 18 months. He just expresses it differently. Louder. With a better vocabulary.
The same applies to me, if I think about it. I have pretty huge problems with authority. Always have. I've been violently fired on several occasions (an employer once threatened to shove a spatula up my ass before screaming "GET OUT!"). I've even been fired by members of my own family. I've been thrown out of classes, sat in more principals offices and corners than I care to remember, and generally fought my way through adolescence like a cornered animal. So is it any wonder I'm self-employed? This works for me.
When it comes to writing, the key is growth, but I'm wondering if there's a fine distinction between "growth OF character" and "growth IN character." I think if you're being true to life, your characters enter the story as pretty much the same people they'll be when the exit the story. Their fundamental character, or essence, does not change much. Instead, the story is a tale of how that particular person adapts to the situation they're presented with, and how they learn to apply or suppress character traits to accomplish their goals. Just like life.
I'm thinking now of Mr. Darcy in Pride & Prejudice. Darcy entered the story a proud, conceited member of the upper class, but he was also a gentleman and he was generous of nature. He exits the story as the same guy, but I think one of the subtexts of Pride and Prejudice is Darcy's assuming the mantle as the master of Pemberley. And that's what Elizabeth teaches him through her initial rejection of him: that first and foremost, he must be a gentleman to the people whose station is "so far beneath his own," as he puts it. His pride isn't defeated, it is shaped into nobility.
It's an interesting question, and it's a challenge. The question is not "how will my character be different at the end" but "how will my character learn to adapt to a new normal."