Not entirely true, although certainly advisable.
I used twist-top bottles for my first 5 or 6 batches of brew and I had consistent carbonation throughout. I should mention that I used a bench capper, which in most cases provides a superior seal to that which can be achieved using a "wing" capper.
Primary: Edwort's Apfelwein
Primary: Brewingcentres Pale Ale
Primary: Brewcraft - Cheap 'n' Shiddy Bavarian Wheat
Kegged: Brewcraft - Cheap 'n' Shiddy Bavarian Wheat
Kegged: Brewcraft - Enhanced Dutch Lager
On Tap: Brewcraft - Irish Stout