"A sign of" something is not the same as "definitively the cause of" something.

A runny nose is a sign of a cold, even though you can have a runny nose without a cold.

Logically -- scientifically -- a runny nose might not be said to be "a sign of a cold". That is, it is not sufficient evidence to indicate a cold. When paired with other data, it may contribute to a diagnosis. It's not unrelated.

Similarly, an imaginary friend is not "a sign of" loneliness. On its own. When grouped with other data, maybe together they are.

It's just a difference in language usage. "A sign of X" might be taken to mean that on its own, X is implied. Or it might be taken to mean that it can be a contributing factor, but on it's own is meaningless.