They don't fail to tell law enforcement after paying kidnapping ransoms and don't consider the perp to be law-abiding person. Also if a kidnapper was ever located domestically there'd be about a 0.00001% chance of the person getting a payout.
A myth.
Here's a book from an ex FBI hostage negotiator. It narrates some real case stories from the inside, it's well written and quite interesting. https://www.amazon.co.uk/Stalling-Time-Life-Hostage-Negotiat...
So “outcomes are worse if you don’t” is not relevant. Several times as many terrorism incidents with better outcomes on average is not what most people would consider effective anti-terrorism.