I also think the two paragraphs preceding the quoted section in the OP are important to look at:
On top of that, we have also embarked on a fairly extensive partnership program. Six or seven years ago, we had, systemwide, maybe 1,000-plus codeshares. Today, we're close to 10,000 codeshares, building up partnerships with like-minded carriers. It goes beyond the Star Alliance: Virgin America and JetBlue, for example, are partners.
Why is this important? Let's take a concrete example. We have an extensive, joint-venture codeshare with Lufthansa, which includes a revenue-sharing component. That's good for customers coming from Singapore who want to travel to Europe where Lufthansa has great regional connectivity. And it's equally good coming to Singapore, which has similarly great connectivity, when flying from Europe. And we both can provide a very attractive frequent-flyer program.
We are very happy to discuss this with United as well; United is a Star Alliance partner, and I think a cross-alliance partnership is a bit difficult.
But there are also those who are not in an alliance, for example JetBlue, Virgin America and others. So we will continue to look for opportunities and cooperation with United, but we would also be open to work with others if the United route network is not available.
And from what I read from his statement and from Bloomberg's article a few days ago, North America is arguably SQ's most important market, or at least the one on which they're most focused. Codeshares and ULH flights are the only ways SQ can competitively serve North America in a way that makes financial sense, and the jury's still out as to whether even ULH flights are suddenly viable with new equipment. So that leaves codeshares as being more important and a lower risk way of growing SQ's rather small relevance in North America.
But what I think is interesting in what I quoted is his focus on revenue sharing. If I'm reading between the lines, perhaps SQ would be "more than happy" to enter into revenue sharing with UA like with LH, but the fact that he cites smaller carriers being more open to cozier agreements if UA "is not available" may signify that UA really isn't all that interested in playing nice with SQ. Seeing as UA started US-SIN nonstop out of nowhere (did anyone really expect it until when it was announced?) when SQ had been saying for a while that SQ was waiting until 2018 to do so seems like UA was giving an F-U to SQ. And really, what does SQ's network really add to UA's? UA already has a pretty robust network into Asia as it is, including India, and it can always lean onto the NH JV for even more onward connections. And SQ doesn't provide any utility into Australia and Oceania in the same way it would to a European carrier like LH, so what else does that really leave?
I also don't buy the "SQ doesn't like UA's product" theory. In the end, it all comes down to cash. SQ would have a lot more to gain financially from a JV with UA, which flies extensively to all over the US and Asia compared to small potatoes VX and B6, which have no TPAC and still only penetrate a selection of US cities compared to UA. And UA probably doesn't want to share any of its revenue (and boy, is UA making money now) with a stuffy legacy carrier in a region with the highest LCC penetration in the world (SQ's CEO's words, not mine).
That's just me trying to read the tea leaves, but it seems like SQ would gain a lot more from a revenue sharing JV with UA than UA would. I guess it's not unlike what Mariah Carey thinks