Switching tenses in the story telling?

Hi. Is it correct (natural?) to switch tenses in the middle of his or her talking about what happened as seem to have been done here? Please look at the last sentence of the quoted saying.

This is from a joke named "Busy In Heaven" under the category of Religious Jokes in the thejokeyard.com site:

The second man comes up and Peter explains to him about heaven being full, and again asks for his story.

"It's been a very strange day. You see, I live on the 26th floor of my apartment building, and every morning I do my exercises out on my balcony. Well, this morning I must have slipped or something, because I fell over the edge. But I got lucky, and caught the railing of the balcony on the floor below me. I knew I couldn't hang on for very long, when suddenly this man burst out onto the balcony. I thought for sure I was saved, when he started beating on me and kicking me. I held on the best I could until he ran into the apartment and grabbed a hammer and started pounding on my hands. Finally I just let go, but again I got lucky and fell into the bushes below, stunned but all right. Just when I was thinking I was going to be okay, this refrigerator comes falling out of the sky and crushes me instantly, and now I'm here."