Step 1: Set up the elimination.
Again we are hunting for the one false claim about testicular torsion among four statements.
Step 2: Think through what torsion actually is.
It is a mechanical twist of the cord cutting off blood flow, not an infection, so any finding that points to inflammation or infection should feel out of place in a list of torsion facts.
Step 3: Weigh the Doppler claim.
No blood flow seen on Doppler in a testis with sudden pain strongly supports torsion, so this statement stands as true.
Step 4: Weigh the pyuria claim.
Pus cells in the urine come from infection or inflammation in the urinary tract, not from a twisted cord. If anything, finding pyuria should make a doctor think more about epididymo-orchitis and less about torsion, so saying pyuria assists the diagnosis of torsion is backwards, and this is the false statement.
Step 5: Weigh the remaining two claims.
Both testes often share the same loose attachment that let one of them twist, so surgeons fix the other testis too, during the same operation, to stop it from twisting later. Also, lifting the testis in torsion does not ease the pain and can even worsen it, which is the classic negative Prehn's sign, separating torsion from epididymitis where lifting usually helps. Both of these statements are correct.
Step 6: Conclude.
\[ \boxed{\text{Presence of pyuria assists the diagnosis}} \]