As we are typing of brake lines, I really need someone to tell me that the "T" in question requires any kind of washer to seal the connections.

Whereas my thinking would be that the either the "T" or the pipe flair are not mating correctly and thus leaking. Any attempt to seal with washers might indeed work but surely would be regarded as non standard and a risky bodge, perhaps more so if the connection has been over tightened or the threads in both items in the connection are of a mis-match..?