It is important at this early stage to reexamine our concept of what singing really is and more precisely, what a sung note really is. And of course a connected series of notes, a sung phrase, as that is in many ways a basic chunk of singing.
Singing is not just the words on the notes. If we just pick out a song we might find a lyric like this:
"I wanna swing from the chandelier"
We might even write down the notes
Now the question: Where is the singing? Is it in the words? In the meaning of the words? In the melody, on in the notes? Of course, none of these things. Singing is about sound. So if we listen to Sia on the track mentioned, we will hear how she shapes and works the sounds of the lyrics around the notes of the melody to create the sonic art that is singing.
A sung note has many attributes: Timbre, Attack, Loudness, Modulation, Sustain, Noise (air), and of course Pitch. More attributes could be described depending on level of detail.
Each of the abovementioned attributes is, pretty much, equally important. If any one of them is seriously off, the note (and the phrase, maybe even the song..) is ruined.
So the take-away fact here is that we have far more to think about than just the pitch, and we need to rely on the many inbuilt systems the body has for singing in order to achieve success. Pitch is not the difficulty: the ability to hit 'all the notes' comes early in the learning process.