I have had friends who seemed to want to one-up me in weird ways, yeah, but not as drastic as your friend. I did hear a weird story from another friend of mine. Someone she knew had some really strange health issues - I forget what her symptoms were, but they were bizarre and she had extreme fatigue. She was talked into going to the ER where she learned that she had an extremely rare form of cancer - she wound up staying for two months.

A few days after her diagnosis, her sister demanded that she also be tested for the cancer, even though she had none of the symptoms. Everyone around her thought it was a strange bid for attention.

So no idea why people do this, but your friend is definitely not the only one.