> draw what they need to from the circuit

I don't think this statement refers to single components.Put too much current through the LED it will be damaged or destroyed.If you put too much voltage across it,the same thing can happen.

An assembly or a system of components,or,to be more specific,the entire circuit of a device like a mobile phone or a laptop has the ability to protect itself,more than a single component has(for example:a transistor).It can shut down charging if it doesn't like the input you give it.Given a correct voltage,it will indeed draw the current it needs.

However,note that no device is invincible:at some point,with too big or too high current or voltage you can damage or destroy them completely.Let's say you have a step up converter which has no feedback from its output and you want charge your phone with it.If the phone doesn't accept it and interrupts charging,the output voltage may jump to a high value and burn it.