It's not a misconception, it's the definition of motivation.
The misconception is using the word "motivation" only for intrinsic motivation. If you have a gun pointed at your head, you'll be quite motivated to do whatever the person holding the gun tells you. External motivation can be extremely powerful, it just doesn't last long.
> Act first, become motivated later.
You're right. You need some external motivation to start "acting first". There are four types of external motivation (from more external to more internal) – fully external, introjected, identified, internal. Rewards and punishments are the first (external), rewards/punishments "in your head" (aka image of your parents telling you to do homework or you don't get TV time) are the second (introjected), part of your identity ("I'm Muslim, thus have to wear hijab") - third (identified), and "I truly believe I have to do something" is fourth (internal). Internal type of external motivation differs from intrinsic motivation (which is defined as "acting because I enjoy the process", and you can truly believe you have to do something but not enjoy it).
Discipline and self-discipline are somewhere between introjected and internal types, but it's essentially a codename for external motivation nevertheless.
In many cases you really want to instill intrinsic motivation in kids/athletes/employees/etc. But you need to "act first" and repetitively link it to the positive emotions – and that's where external motivation (and discipline) can be used strategically to create intrinsic one. Unfortunately a lot of people/fields/disciplines get stuck in the external reward systems and don't use it strategically.