It's completely unwarranted because you essentially can't have inflation in a depression. There isn't enough demand competing for supply to raise prices. That is why governments and central banks usually try to inject money into the economy in lean times, and take it out to keep it from overheating. It's the basis of essentially all macroeconomic management.

The real danger in times of low demand is a deflationary spiral. Those are fiendishly hard to get out of, as the last few decades for Japan have demonstrated.