Is it really that easy to make safe cured salmon with a 3 min sugar/salt brine?
There are lots of ways to "cure" salmon. Salt, acid, smoke, etc. Max's comment on going for a longer curing time makes sense. Keeping salmon out of the bacteria temp range, keeping it dry (salt and sugar absorb water, but only salt kills) and verifying it cured properly or cooking thoroughly is your best bet from getting botulism.

http://www.fao.org/wairdocs/tan/x5902e/x5902e01.htm
https://www.theatlantic.com/health/archive/2013/12/how-not-to-die-of-botulism/281649/