There is a particular sense in which this is true. I’m no Quranic scholar, but this particular facet of spiritual understanding is echoed in other traditions as well. There’s this exchange from the Zen tradition, for instance, that aims at the same principle:
In T’ang era China there was a hunter named Shigong who was out hunting deer one day. He crossed paths with a Zen monk named Ma Tzu and asked him if he had seen any deer.
Ma Tzu asked, “Who are you?”
“A hunter,” he replied.
“Do you know how to shoot?” Ma Tzu asked.
“Of course I do,” answered the hunter.
“How many can you hit with one arrow?” asked Ma Tzu.
“One arrow can only shoot down one deer,” said Shigong.
“In that case, you really don’t know how to shoot,” Ma Tzu said.
The hunter then asked Ma Tzu, “Do you know how to shoot?”
Ma Tzu replied, “Of course I do.”
“How many can you kill with one arrow?” the hunter asked.
“I can kill all of them with a single arrow,” answered Ma Tzu.
At this, Shigong said, “The beasts have life as you do: why should you shoot down a whole flock?”
Ma Tzu said, “Since you know this so well, why don’t you shoot yourself?”
The point is that our sense of separateness, of individuality, is only one way of seeing reality. It’s a valid and necessary way, but not the whole truth. Many different religious traditions have tried to open people’s eyes to another way of seeing in which there is no such separation. From that perspective, each being is all of the others (which is really the same as saying that there are no “others”).
Both of these perspectives have a measure of truth, and neither by itself captures the entirety of the truth.