I could understand that study. When one roots their personal value in something external, like a measure of success, they spend their whole life working ridiculously hard and sacrificing everything to validate themselves based on the measuring stick of that externality.
The only problem is the measuring stick always keeps growing taller. So what is "success" to that specific individual when they can't enjoy it or even recognize it as "good enough"? Others will tell them they're an amazing success, but they'll never believe it was enough of a success. That definition of being more successful is based on the others' perception.
Not only that, but you'll notice the study did not say internalizing success means you'll be less successful. It's possible to be content by valuing yourself in foundational principles like "hard work, integrity" etc. and through that achieve both success and happiness.
I'd be interested to see that psych study, but it does seem pretty common sense, though. The more you value an outcome in life the more you'll spend your life chasing it - and the higher probability you'll reach it.