Sorry, but it's not possible. Try to set density to zero in material editor, it will change to 0.001. See enclosed picture.
The change is because of the Protein(Autodesk Material Library) introduced into Inventor 2013, which can be shared with multiple Autodesk products, but if you now only use Inventor and want to take use of the legacy materials you can just uninstall the Protein, and then try to use the legacy materials which allows to set negative density.
I double checked, you're right, the density has limits, if you input a value is out of lower/higher range, it will just use the lower/higher value instead, and the lower value is positive. And so if you need to calculate mass with zero value I think you can try to override the mass.
Thanks, of course this is possible, but this is not real solution. I think that if we have material catalogue and there properties of materials we should use it. There is a lot of ways how to solve this new behaviour, problem is that Autodesk does not document these changes and nobody of designers can belive that model which was correct in summer is correct in winter (because zero is not zero). And this is what is the matter.
Thanks for your reporting it. btw, do you think a large range is needed or we don't have any range?