Ok, Here are some totally guesswork figures some that I would think underestimate the final answer.
If an assumption is made that each individual Concorde averages just one round trip a week scheduled, and during each round trip 4 hours are spent at supersonic speed that's 208 hrs supersonic per year per Concorde. 16 Concordes over 25 years amounts to 83,200 hours supersonic during the career so far of this brill' machine.
That's a lot of potentially underestimated hours, and doesn't include the pre-production machines or other non-scheduled flights. I think the original claim holds water.