As the others have already stated, this is vital if you want to avoid MAJOR (think in terms of a couple of thousand $$) engine damage.
That being said, I wonder why someone would doubt the manufacturer's recommendation for timing belt replacement based on elapsed time--or any other scheduled maintenance items based on elapsed time. Honda would like you to buy another vehicle from them, but if you have a very negative experience with the longevity of the car (like what would result from a snapped timing belt), you would be unlikely to buy another Honda. As a result, it is always prudent to believe and to follow the manufacturer's maintenance recommendations carefully. This leads me to wonder if skepticism has led the OP to ignore other elapsed time recommendations for maintenance.
Ignoring a dealership's maintenance recommendations is frequently a good thing. Ignoring the vehicle manufacturer's maintenance recommendations is foolhardy and is sure to lead to more expense in the long run.