Step 1: Understand what the question wants.
We need the FALSE statement about urethral injury, not the true one. Three of the four statements are accepted facts, and one goes against standard teaching.
Step 2: Check "rare in women".
The female urethra is short and mobile, and it is well protected within the pelvis, so it is injured far less often than the longer, more fixed male urethra. This statement is true.
Step 3: Check "posterior urethral injury occurs in fracture pelvis".
The posterior (membranous) urethra is fixed at the urogenital diaphragm. A pelvic fracture, especially one with a shift at the pubic symphysis, can shear this fixed segment and tear it. This is the classic mechanism taught for posterior urethral injury, so this statement is true.
Step 4: Check "blood at the urinary meatus is diagnostic".
Blood dripping from the external meatus after trauma is the single most reliable clinical sign of a urethral injury and should always trigger further evaluation before any tube is passed. This statement is true.
Step 5: Check "immediate catheterisation is indicated".
This is the false one. When a urethral injury is suspected, passing a catheter blindly can convert a partial tear into a complete transection, push in infection, or create a false passage. The correct first step is a retrograde urethrogram to check whether the urethra is intact before any catheter is passed. So immediate catheterisation is not indicated, it is actually contraindicated until imaging is done.
Step 6: Final answer.
The statement that is NOT true is that immediate catheterisation is indicated.
\[ \boxed{\text{Immediate catheterisation is indicated}} \]