Yes, we presume the CSO had meaningful and accurate information about whether the message(s) left SingPass's systems on their way to your phone. That's a presumption, not a guarantee, but let's assume that much is factually correct. SingPass most probably does business with an intermediate SMS service provider not named StarHub. What happened there, we don't know.
Sure, SMS text messages are sometimes delayed, sometimes never delivered. For a variety of reasons. It's a fairly unreliable way to deliver a message. That's why SingPass is sensible enough to avoid routinely using SMS.
I haven't found any non-anecdotal data evaluating whether Eight (and StarHub) are more or less reliable than other carriers when it comes to SMS text message delivery timeliness and reliability. I'd love to find such data.