Can weathering change the composition of something so that it appears different?
Yes, weather can and probably will change the composition of materials and make them different. 

However, forensic analysis usually takes that into account. There are some properties that might change because of weathering (you shouldn't compare water content, for example), but others won't. According to the sample article, the difference was found in the chemical composition of the paints.  Since details were not disclosed, one can only guess what these differences are, but some possibilites are:


Presence or absence of metals in the paints
Substances that wouldn't appear or disappear because of wheatering
Different isotopic ratios of elements
Traces of the solvent indicating they were not the same
Probably others


Assuming the analysis were performed correctly, it is usually not hard to say two samples are different. On the other side, when the results are similar, you can hardly say they are equal, but only that they match and that no differences were found.