The public Land Transport Authority built and still owns most of the assets, and enacts strong regulation for the duopoly of service providers (SBS and SMRT) - not only on service levels, but also on operational processes. Even so, there's awkward UX quirks on the boundaries between lines run by the different companies.
If anything, the Singapore MRT runs closer in spirit to a US taxicab system - that is, surprisingly regulated on a global scale.
Comfortdelgro is certainly widely owned - but they're into busses and taxi mainly, not infra heavy stuff like subways.
For various reasons, Governments will make state owned companies publically traded. That doesn't mean they're not going to toe the government line in decisions if it has majority stake.
I wasn't aware that SMRT was bought out by the government recently (the last time I rode the MRT, last year, it was still private). It doesn't seem that the buyout was orchestrated as some sort of bailout, especially given that the systems seem to be solvent enough to support at least one for-profit. It, then, remains to be seen if refolding SMRT will result in a net degradation or net improvement in services... This will be an interesting 'control' experiment.
It's too bad. Because singapore, which arguably has the world's best (or maybe second best, after Seoul) public transit system, is basically an entirely privatized system.