I think you're half right. But there
are cultures in which people save money. (You can just run a web search for "savings rate".)
My hypothesis is that "human" nature does play a role, specifically a very general phenomenon in animal psychology called "observational learning". If you see people around you who saved money and it worked out for them, you're more likely to imitate those people. Saving money probably isn't instinctive for the vast majority, but that doesn't mean it's unattainable.
Taking the contrapositive, if we look at cultures where people don't save money, it's probably because of a lack of successful role models. Saving money hasn't worked out for people in that culture in the past, so there's nobody to imitate. There are always going to be a few people who do save money, but if they get wiped out by medical debt, rampant hyperinflation, or some other systemic crises, or if the country's bankruptcy laws are so generous that their spendthrift counterparts ultimately live better than they do, then their behavior is less likely to catch on.
In the US, savings culture has been decimated by years of QE and ZIRP, so the people who poured all of their money into housing and stocks did better than the cautious types. Skeptics have claimed for years that this will lead to an awful hangover. We'll see.