On my WRX the belt is due at 105K as you say. I will not replace it before then. If you are concerned, as you seem to be, then it's a one-way street: have the belt inspected. Frankly, you should price mere inspection vs. outright replacement and see what makes most financial sense. If the fee your mechanic charges is quite high compared to the fee for changing the belt, well then go for everything.
BTW, not to raise your concerns but if you do not have a full service history for the car, you should keep in mind that the odometer readings on these cars are stored in the instrument cluster, not on the ECU. This means that swapping clusters instantly gives a new odometer reading. Are you sure your car has 62K? Belts should not disintegrate like that, even "external" belts like the alt/steering belt.