It's not about how much money a person has, but it is about being able to succeed at your intentions. And certain topics - like money - are usually associated with deep emotions.
If you're poor, and never give more than the merest passing thought to money because you're happy with your system, then you can count it as a success. But if you find yourself repeatedly making simple resolutions - like trying to live on a budget, avoid overdrawing your account, pay your bills on time, etc - then part of you is interfering with your intent.
Even though I don't make much more money now than I did a couple years ago (because, ahem, I am addressing a shadow complex about demanding a good sized raise!), the difference between my money situation now, and a year or two ago is very big. I used to waste a lot of time looking for cheaper solutions for every one of my wants and needs, I used to overdraw my account fairly regularly, I had a hard time budgeting and paying bills on time.
I started to realize how much I had invested in staying "poor" or keeping a poverty-driven mentality. I addressed the 'shadow' components, and then committed to change. Now, if I can afford something I need or want, I buy it without endless price comparisons and bargain-hunting. I don't overdraw my account hardly ever. I budget, and pay bills on time. Discussing my finances doesn't trigger anxiety.
I don't believe that 'anyone' has the potential to be 'rich'. I doubt that it's everyone's True Will. But a healthy person should, IMO, be able to make a reasonable, rational, doable resolution in any area of their life and accomplish it. I've watched myself (and others!) with important goals and dreams that just require a small initial step, delaying and procrastinating the undertaking for years simply because the shadow isn't addressed properly.