There are many alternative phrases to "The story has no element of truth," ranging in formality and directness. Here are some options:
More Direct Alternatives
These phrases directly state that the story is entirely false:
The story is completely false.
The story is entirely untrue.
There's no truth to the story.
The story is baseless.
The story is utterly fabricated.
It's a complete fabrication.
It's an outright lie.
It's pure fiction.
Less Direct / More Nuanced Alternatives
These options suggest varying degrees of untruth or unreliability:
The story is highly questionable. (Implies doubt)
The story lacks credibility. (Suggests it's not believable)
There's little truth to the story. (Implies a tiny bit might be true, but mostly false)
The story is far from the truth. (Emphasizes its deviation from reality)
The story is inaccurate. (Suggests it contains errors, not necessarily malicious intent)
The story is unfounded. (Implies it has no basis in fact)
The story is unsubstantiated. (Means there's no evidence to support it)
It's a baseless claim.
It's pure conjecture. (Suggests it's based on guesswork, not facts)
Informal Alternatives
These are more casual ways to express the same idea:
It's total nonsense.
It's garbage.
That's a lie.
No way that's true.
It's made up.