“Qui” is the interrogative pronoun which inquires about a person. Because you can’t “dire” a person¹, the only logical grammatical function “qui” (without a preposition such as “à”) can have is to be the subject of the verb “dit”. Now take the (incorrect) sentence

*Qui a-t-il dit ça ?

“Qui” is the subject. What function does “il” have? Well “il” is always subject! So in this sentence, “dit” has two different subjects: “il”, who refers to a known male singular person, and “qui” which refers to and inquires about the unknown author of “dit”.

This is obviously incorrect.

Now, when a verb is transitive and can have a person has a complement, the structure is correct.

For exemple, “inviter quelqu’un”:

Qui a-t-il invité ?
Whom did he invite?

1. In English, you can “tell someone something” or “say something to someone”; in French, you can’t “*dire quelqu’un quelque chose”, you can only “dire quelque chose à quelqu’un”.

La règle est d’avoir un sujet au centre de l’interrogation.
Dans la phrase « qui a-t-il dit ça ? », il y a deux sujets représentés par :

• Qui

• Il (et son -t- qui représente simplement la structure interrogative).

On doit donc en éliminer un, ce qui peut donner respectivement :

• Qui a dit ça ?

• A-t-il dit ça ?

Cependant, à la deuxième phrase, on peut remarquer que le sens de la phrase change.
Donc si on suit la logique, on choisit la première proposition.

This would be correct, although with a different meaning (Who did he tell that to ?) :

À qui a-t-il dit ça ?