Is Kramer really Batman?

For the uninitiated, in S05E20 The Fire, Kramer tells a great story about taking a severed pinky toe to the hospital for reattachment. He fights off a mugger and drives the bus after the driver gets knocked out, prompting George to proclaim him 'Batman'. Here is the scene

So here Kramer tells a story of bravery but then, in S07E06 The Soup Nazi, he is guarding Elaine's armoire when he is confronted by Cedric and Bob, the gay street toughs. He is very intimidated and afraid. Later in the episode, he and Jerry run away from another confrontation with Cedric and Bob. Here are the scenes

So did Kramer make the whole bus thing up or do you think it really happened the way he told it?