That’s just what people with money tell the people without money to stop them from rioting. We have research that suggests that money indeed does buy happiness.
https://knowledge.wharton.upenn.edu/article/does-money-buy-h...
There are exceptions of course. Some people are just predisposed to being unhappy no matter the circumstances, but generally speaking more money directly correlates to increased life contentment.
I think it's a bit more nuanced than that. As I understand it, happiness increases for most people as their income increases. However, this doesn't mean that a person is happy overall since there are other factors. So, it's not that money can buy happiness in a binary sense, but it's a factor and often a significant one.
The article even ends with this quote from one of the authors of the study (emphasis added):
“Money is not the secret to happiness, but it can probably help a bit.”