False.
The vagina is designed to stretch during birth, which is normal. On the inside it feels rough to the touch, which is actually folds of flesh, which concertina out during labour. Afterwards, it usually returns to its normal size. It's a very flexible organ, not only stretching during birth, but also shrinking back to its normal size afterwards.
If you are worried, most doctors will tell you to de pelvic floor exercises before and after having a baby, to keep the vaginal muscles toned. These are called Kegel exercises.
Some women stretch very much during birth and don't do the correct exercises afterwards to help the vagina recover. This could eventually lead to urinary incontinence, which is why it's extremely important to take the time to strengthen your pelvic floor as soon as possible after giving birth, not only for your sex life, but also your health.