Almost ten years later I am having the same problem. I'm getting a -1.31 correlation between two BioClim layers. I think I have found the problem though!
This only happens when I am using modified BioClim data that I had converted to floating point. I was making sample data for students and I wanted to them to be able to see real temperatures in C. So I simply divided Bio10 and Bio11 by 10.0 in Raster Calculator. This resulted in floating point rasters. Meanwhile my elevation and rainfall data (also from BioClim) remain as signed integers. The combination confuses the Band Collection Statistics tools in both ArcMap 10.6 and ArcGIS Pro 2.2.4. In both cases resulting in the same impossible correlation values. If I rerun the exact analysis with only the original signed integer data from WorldClim, it works normally.
So I'd guess Esri needs to add a warning about using different pixel type rasters in the tool.