But then the other part of me says that I clearly have no clue what I'm talking about, there's basically no chance they could stay relevant this long without being on top of it at some meaningful level. And potential quasi monopoly status doesn't quite capture it. So much of finance has been disrupted by technology, you figure if there's finance companies who wasn't disrupted, it must be because they are the technology.
It seems their main software division is in India and in the US it's mostly sales, servers, mobile, and POS support, suggesting that the company is focused on the bottom line and probably could be disrupted. For example Bitcoin is getting more and more prevalent. But it's going to take a while before supporting a new payment network is as easy as an over-the-air software update. And the recent trend in "disruption" is acquihires as seen here.
Apple couldn't even do it with their in-house credit card.
Governments are eventually going to see "a foreign company owning our major payment networks" as a national security and sovereignity risk, especially if we end up in a multi-major-power world. They'll also eventually covet the data and the ability to disable "inconvenient" business. You might see it take the form of a government-mandated account (would Visa/Mastercard have taken off at the same angle if universal, instant direct debits were available in the US?), or just providing a glidepath for local commercial alternatives. Look at what Russia is doing with the Mir card.