I understand what you're saying, but honest question: why is it helpful to add this caveat?
It is very comforting for people who are high on the social ladder to believe in a meritocracy: it lets one their successes are due to their superior character, and those who are on the bottom of the ladder are there due to a failure of character.
Again, if it helps go right ahead.
Interpreted as a literal propositional statement, it's saying "if you have a good attitude, then you will have success". Therefore if you do not have success, it must be because you did not have a good attitude, which is your fault. It's the contrapositive, right?
If success is determined by positive thinking that seems like it strongly implies that success is a necessary and sufficient condition.
Which implies that a lack of success is a failure of attitude.
Admittedly, this is mostly a semantics game of what specifically "determines" means, but to me it strongly implies both necessary and sufficient.
It's true that your attitude and behaviors matter. Competence is usually rewarded, and you should act in accordance with that truth. But it's not absolute. Life is not a meritocracy (whatever that really means).
Or as an old space pirate once put it "never tell me to odds!"
It's not really a caveat, though, is it? It's an entirely false premise, that intent & direction & purpose are irrelevant. That the primary factor that matters is attitude & self-belief. As commenter Zepto rightly pointed out, this article is proposing magical thinking: the conceit that what you want or what you think is the thing that shapes reality all about.
Besides being delusional, it also has all the other obviously bad impact that it's twin the Prosperity Gospel brings: those without riches & success have all failed to be worthy, are all faulty. No matter how hard you work, how good you try to be, judging in Attitude or Belief as the only/primary/core determiner of success doesn't allow for misfortune, or for it to be the world that was wrong. Often, the world _is_ wrong, and only those rebels that hold up their flame & let their light shine are what it takes, what makes humankind & the human spirit so great... but so often those folks are crushed, too. And not for a failure of attitude or belief, nor often strategy nor execution either. Hard things, sometimes, ought be tried & embarked upon, but to internalize success as the judgement of whether the hard thing was right or wrong? That is petty, small, and insufficient. It diminishes the light of the world to require & judge only by success.