Singapore is 281.3 mi², Texas (a single US state) by itself is 268,597 mi². The level of public transit that some countries and cities have and people expect are simply not feasible in a lot of places simply due to the sheer size. And even cities within these states are larger than some countries.
You left out size of population, as well as the place having a size large enough to reasonably need transit. You can have 100 people packed in a single room and that is very dense, but if they are alone on a tiny room-sized planet then public transit won’t make sense. Neither will cars. To go anywhere they need to go straight to rockets. But that’s assuming there’s anywhere to go. Size of population and available places to go also matter.
Point is if you want to get hyper asperger’s about it, you can, but it’s not necessary to have done so because there is implicit information here, and besides, your final claim (density is what matters) ended up being incorrect, because holding you to the same standard that you hold others, you didn’t state all the implicit information.
Knowing that Singapore has a large enough population as we do know because it is well known as a large city-state, we can infer the density from that information combined with the small size. But density is not all that matters.
Shorter distances between destinations encourages walking, biking, and mass transit use. Longer distances between destinations encourages automobile use.
To be more precise I am referring to relative distances within a city. Both density and distances are crucial. Compact cities mean shorter public transit lines, faster trip times, and more efficient use of transit worker labor and vehicles (more route loops per hour and passengers reached per hour). Sprawled out cities have a vicious cycle of more miles/kilometers to cover which means longer trips and therefore less attractive service. The same shifts and vehicle miles serve less people.