I agree with comments here that using distilled water in a battery is the right thing to do -- given the likely nature of available alternatives.
What I mean is that all water purification methods have their pluses and minuses, this includes distilled water. As a simple example, double distilled water exists (although not sold in most places), which should be enough to convince most people that there are contaminants remaining after a single distillation process (even though those are not significant for car battery use).
The OP probably had some kind of RO system at home or otherwise had access to RO water. The usability of that water in a battery DEPENDS ON the details of the RO system. Generally, an RO system removes contaminants based on size (while distillation removes based on boiling point), including very, very small molecules and ions. And an RO system can have (but doesn't have to have) additional components, such as to remove based on charge (de-ionization) and based on additional filtration.
Because of the dependency on exactly what the RO system might be, the simplest, and safest, way for most people is to 'just use' distilled water from a store or other known source.