For fermentation? I'd tend to disagree. +/-1 is pretty good Don't be chumped by any of those controller's claims of +/-0.2 in practice they will never achieve anything approaching this.
By the way, before I was selling bushcraft gear I had a firm making temperature sensing probes so I know there's an industry wide fog regarding temperature accuracy of systems.
Well, there's accuracy and there's accuracy... I certainly don't imagine that any of my thermometers are particularly accurate in the absolute sense (my best instrument in that regard would be my ETI Thermo 20, which is calibrated to UKAS standards and claims an absolute accuracy of +/- 0.4 deg C - it's slightly overdue for recalibration though) but they mostly seem to have pretty good repeatability, which is what really matters. And I also don't imagine that the entire vessel is at exactly the same temperature... I'd settle for +/- 0.5 degrees. Mind you, I'm a bit obsessive...
Just out of interest, what is the optimum temperature for a good ferment?
Depends a great deal on the yeast strain and beer style.