Is it true that silence means more than a thousand words said?

Yes, sometimes silence is the best, in addition to this, silence usually does not force a person to repent or apologise, on the contrary, if a person gives a worse response, his poor selection of words or abuses forced him to apologise for thousand times.

وقیل لبعضہم لم لزمت السکوت؟ لانی لم اندم علی السکوت قط وقد ندمت علی الکلام مرارا

Once someone asked a
wise person, "Why don’t you speak but always remain silent?" He said I never repented on silence but I have repented and regretted many times on my sayings.

I think there are a few sayings that prohibit silence. Otherwise, silence is a hundred thousand times better than those ill-responses that lead to destruction. Here I’ll quote two verses from Arabic poetry that explain the importance of silence.

قد أفلح الساكت الصموت

 كلامه قد يعد قوت

ما كل نطق له جواب

جواب ما يكره السكوت

Indeed the silent & still person has succeeded

His saying is highly regarded (he thinks before he speaks. Because of knowledge & wisdom, he speaks less)

There is no answer to every saying (it is not necessary to respond to every barking dog)

But silence is itself an answer 

Here I” ll refer to an incident that happened to my father. Once he was walking alone in the countryside, there he saw four or five wrestlers exercising in a funny mood near a village tube well. 

All of a sudden one of the wrestler started making fun & abusing my father. Only, because he was thin, smart and weak. But my father Muhammad Ramzan (Poet, Teacher & Doctor) showed no panic and anger at all. When he listened to him, he reduced his pace of walking. And at the corner, where he has to take a turn he stood awhile & came back calmly & quietly and said, "I thought there is no one to listen to these abuses. Now I am back here to quench your thirst. I"ll stay here till you are fed up."

When others heard this statement, they started to abuse their fellow, "Why are you annoying a noble person?" And they apologized from my father saying he is a mad person. Do not heed him. Thus my father ashamed the wrestler with the powerful tool of silence. This is a true story, in which silence gave its answer stronger and more powerful than words.