There are rules and conditions which govern our lives some very obvious and other not so.
If a Muslim woman wishes to go and watch the Olympics and she feels comfortable wearing a burkha then as longs as security issues have been resolved by a female checking the person wearing the burkha in the same way as everyone else attending the show then thats fine.
On the other hand if she wishes to take part in the Olympics as an athlete then she clearly can not take part wearing a burkha as that will simply put her life in danger. She in that instance has to make a decision and do a priority call - does she wear her burkha and give up her desire to take part or remove her burkha and take an active part in the Olympics?
Therefore there is no justification issue here as it is a personal call that has to be made based on what is feasible wearing the burkha and what is not.