Reliably? That all depends. It won't match it 100% because the provider will always be in power and as such have the advantage with the STB. It also depends on your TV provider and if they support the TV Everywhere initiative to allow you to sign into a TV Stations app with your service provider credentials. For example, I have AT&T and I can sign into the Comedy Central app to watch shows on demand but my friend has Comcast and they do not allow you to do the same. Also, not all channels have an app available and not all apps have a Live TV option.
Another option is to subscribe to a provider that has their own tvOS app to watch tv and has a guide like, SlingTV or PlayStation Vue. Those would be the best alternatives that resemble a STB experience.
Lastly, there is an app called Channels that works with a piece of hardware called HomeRun TV Tuners. If you're provider is cable based like Comcast, you can rent a piece of equipment called a cable card. You can install the cable card into the HomeRun TV Tuner to get access to the channels in your cable package through certified devices/apps on your home's network. Channels is one of those apps and runs on AppleTV. For Windows you can use Windows Media Center or the free HomeRun software from their website to watch TV. You can also use a TV Tuner from HomeRun that does not use a cable card and instead uses an antenna(sold separately) just to watch the local channels available for free over-the-air.