I don't buy it. I don't see how a transformer could fail open, seeing that there is no galvanic connection between the primary and secondary coil. Moreover, a step-up/step-down transformer will have a fuse in it that will prevent excess current flow so, even if it were to fail open, the fuse would blow. If there is a short against the chassis of the transformer (primary or secondary side), an RCD (residual current device, aka earth leakage detector) will trip instantly. (Most households will have one of these installed by now. If not, get one installed immediately. These things save lives.)
The one thing that could cause problems is the different mains frequency. But the heater in the Anova doesn't care about that, and the electronics almost certainly use a switching power supply, which doesn't care about frequency.
The fact is that, if you have a transformer that is large enough to handle the load, it will work, period. The Anova can't tell where the power comes from, nonsense about voiding warranty from the manufacturer notwithstanding.