That's an awful story, and I can completely see how having something like that happen to a family member would put someone off trampolines completely, but I don't think it should put you off completely. A mini trampoline is much safer than a regular one - you wouldn't be turning somersaults or bouncing very high, and the trampolines sold for home exercise generally have the elastics covered to avoid trip hazards.

Most trampolining accidents involve children, often when safety guidance hasn't been followed properly. You're a responsible adult who would take proper safety precautions, so I think the risk to you would be minimal.