It's not true per say, but it is in theory.
If you never cut your hair:
When hair splits its keep splitting moving back up the hair shaft, meaning hair gets whispier, finer, shorter from the length, as you hair still grows at the root at the same speed, your hair 'appears' to stop growing or slow down, this is because its breaking off.
Regular trims:
You cut off the damaged dead ends (half an inch) as your hair has grown about an inch to an inch n half in this time you are left with half an inch to an inch of healthy hair that is strong and not splitting, then 6-8 weeks later have another trim, cut of just the dead ends and keep doing this your hair will grow longer faster and stay strong.