I am using Joomla 2.5.2 & 3.

I have tried multiple templates: the ones included with joomla, 2 free ones I downloaded and my own custom built one (which has no overrides or framework stuff in it).

This issue still persists for me. Further assistance would be appreciated.

Let suppose the you have select the "JA Purity" templates.

When you create the website with the "whole sharing", this mean that the "/templates/ja_purity" directory is used.
When replacing the content of this directory with the content of another template, this will be the new template that is used.
So if you rename the "beez" into "ja_purity", you get the beez template.

Remark: on Joomla 2.5, some extension have their parameters saved inside the DB and no more read from the "params.ini" file. In this case, the back-end will not reflect the correct template parameters.

When you mention /templates/ja_purity are you referring to the master templates folder or the slave templates folder?

I make reference to the specific "/templates" of each slave sites.