Absolutely positive...
Seems Brennan dismissed the idea that it wasn't a suit right away so as to make it clear that it wasn't an SS or FBI agent; a part of security that, as far as he knew, might have been assigned to buildings in the area.
As well, one would think that removing the shirt would give the shooter a little more freedom to maneuver during the shooting sequence.
Re the dingy Tshirt, he may have looked...
comfortable.
(Like the guy in the 'date' ad haha)