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Do the TUEC have the athlete present
No, they take evidence from the referring doctor, which can be quite detailed medical history. In the specific instance of asthma medication, in order to get a TUE for one of the drugs which needs one, you have to demonstrate that you have tried the ones which don't need a TUE and they don't work for the athlete in question. Similar tests apply for other conditions, since a TUE is only ever issued if there is no alternative effective treatment which doesn't require a TUE.
It needs three doctors to agree, your referring doctor and two out of three on the TUEC :)