This the correct way to look at it. Just as the person spending 5 years working on this will have learnt many things which will be useful after this problem is solved, you have to factor in the training cost (sure it's only done "once", but that is the same for the person too once they jump on the next problem).

The model wouldn't not be able to solve this without all the training leading up to the actual execution, so counting only the tokens of the execution doesn't give the full picture.