It's a kind of 'open' secret that a lot of what's on display for the Classic Doctor's are replicas. The big deal topic when it opened was how the 6th Doctor coat is clearly a Cloth Ears replica though they usually deny this. Using the Pertwee convention jacket vs an on screen one also feeds into this. Tom Baker's scarf was also always a Replica - though they swapped out to a better replica early on.
This decision came from the fact that these costume are not only on display to larger crowds then before but done so *without* ropes or any kind of barrier (glass/railings etc) between the observer and the items. Because of the greater chance of the costumes being stolen or damaged there were more replicas used then originals (though some still are originals). That's why this was done. As far as I know the BBC DO have an original of Pertwee and Colin's coats, but prefer to have them in safe keeping. Personally, I can't blame them.
The McGann costume at the Experience is the most obvious example of a 100% replica (the BBC did not own the original at the time the Experience was mounting up so that was their only option).