Just because NETS terminals can accept UnionPay doesn't mean that the merchants have it enabled, since the fees for credit card acceptance are much higher than the fees for standard NETS transactions.
Yes, that’s what “many haven't configured their NETS terminals this way” means. That’s the why.
Also, looking at the Wikipedia article, I think the UnionPay reciprocal agreement only applies to Discover and Diners Club in China:
https://en.wikipedia.org/wiki/Card_reciprocal_agreements
It’s up to UnionPay to decide whether to allow cross-network transactions for particular cards, card types, and issuers homed on its network. And what types of transactions (card present v. card not present, merchant codes). UnionPay has all sorts of extra oddities in these respects. A Diners Club branded card might actually do a little bit better across the loosely federated network, but YMMV.
In practice, if you want to use a UnionPay, Diners Club, or Discover card, try using it as if it were one of the other logo cards. For example, if you see a merchant that accepts Discover (and is silent about Diners Club) but have a Diners Club card try using it as if it were a Discover card. Chances are at least decent it’ll work. But if it doesn’t work be prepared to pull out your Mastercard, Visa, or American Express card.
I should mention that JCB is also part of the same loosely federated network. So if you see a merchant with a JCB logo then there’s a decent chance your Diners Club card will work. There are also some single country networks where your Diners Club card will probably work. Examples: RuPay accepting merchants in India, BC Card in South Korea. But I don’t pay too much attention to those because Diners Club cards issued in Singapore aren’t great cross-border cards in terms of fees. Cards like the Trust Bank credit card (a Visa card) are much better in that respect.
I’ve had the best luck with Diners Club cards issued in Singapore at card present merchants that have a Discover logo somewhere, such as on the merchant terminal itself. That combination seems to work pretty consistently even if you don’t see a Diners Club logo. Which makes sense because Discover and Diners Club International is now under one network operator (U.S. headquartered Discover Financial). Beyond that it’s more iffy since you’re dealing with the loosely federated network. YMMV.