Why is the verb "tocar" used here?

Why is the verb "tocar" used here?
 

I have the passage below, and the person speaking in the bold sentence thinks the person she's talking to is a nurse who has come to give her pills. And I feel sure she's saying "I don't take the pills for another two hours", but I don't see how "tocar" makes sense here, and can't find other examples of this usage.


"—No me tocan las pastillas hasta dentro de dos horas —protestó sin mirarme—. Me fijé en que la flor que le di antes de marcharse de casa estaba en una mesita junto a la cama. Por ella no había pasado el tiempo. Los pétalos, las hojas y el tallo lucían como si la acabaran de arrancar en ese momento, pese a que sabía que aquello era imposible. Pensé que habría otra azucena en el jardín y que alguna de las enfermeras le hubiera traído otra al marchitarse la que yo le di. Era la única explicación a este hecho. "

When used like this, the verb means that it's the time or the turn to do something.

- ¿Te toca trabajar este sábado? -> Do you have to work this Saturday? (These persons don't always work on Saturdays, but this may be the time they do.)
- ¿Me toca sacar una carta? -> Is it my turn to draw a card?
- Te toca jugar. -> It's your turn to play.
-¿A quién le toca cantar? -> Who's next to sing?
- Ya toca llevar al perro al veterinario. -> It's already time to take the dog to the vet.
- No me tocan las pastillas hasta dentro de dos horas. -> It's not time to take the pills yet, but in two hours.