Unfortunatly, the Dissolve tool in ArcGIS always dissolves the geometry into Multipart features and then (if you want) breaks it into Singlepart features - which works properly "most of the time". To be sure, always run the MultipartToSinglePart tool on the Dissolve tool output.
So more direct to your issue.... As you disscovered, the Dissolve statistics always describe the Multipart shape - not (like you might think) the derived Singlepart shapes.
There is a work around though. The idea being that if you can tag yourt input features with a sort of unique spatial ID and Dissolve by this derived ID value, then your statistics come out the way you envisioned: describing the single part features. See attachment for latest rendition of some Python code that I wrote that does just that.
Yep - Those would be a Data Type of String.
If you still want this to be improved/resolved, please vote here:
Make the dissolve tool smarter when specifying not to create multi-part features.