It's much simpler: Private Banking is offered for a profit, not because it is in demand. If an international bank can make more black ink stateside rather than Samoa, even if the risk/reward ratio isn't that different, the larger bank chooses the more profitable market to distribute it's loans. This puts Samoa in an awkward spot where they have a dearth of services, despite demand, simply because
every bank made this analysis. It's classic Tragedy Of The Commons.
A public bank, in contrast, does not have to put this absolute profit first, giving them the flexibility to enter markets where they might not be as successful, but they don't have nearly the competition for their services. Additionally, since this is operated by the state, they can benefit from business loans and interest as another form of revenue, giving them room to cut taxes or improve services.
EDIT: As consolidation creates both larger businesses and larger reserves of capital, this causes the bank to make more conservative loans. They must play more defensively. As these banks retreat from "riskier" markets, it leaves genuine demand behind. Look at the article's description of "predatory lending" near the top of the article.
Because there is this pent-up demand, a local bank could open a branch that captures some of that demand, and incentivizes locals with higher returns than the international bank because they can charge a higher interest rate. But the IntBank wouldn't still enter this market because the size is still too tiny to warrant their attention and/or the interest rates locally don't move the needle in their global reserves. It's literally too small to be worth the effort.