Yes, I think that is the where the debate is over the exact nature of things. Fission happens spontaneously, even the bismuth in Pepto Bismol has a bit of a fission going on, slowly decaying into thallium.
²⁰⁹Bi decay to ²⁰⁵Tl is alpha decay — the bismuth nucleus splits into an alpha particle (helium) and a thallium nucleus. I think you’d be hard pressed to find a nuclear physicist or engineer who calls that “fission”.
Here’s the Wikipedia article on fission. It’s a rather different process:
