I've just taken over on a project that involves an installation of JMS multisites, purchased from JMS, as the last employee has left.

I'd like to know if it's possible to actually run multiple sites from one single Joomla installation.

I've noticed that the tutorial procedure from the manual and videos leads to subfolders with Joomla installs inside them.

This being the case, can I have everything run from just ONE installation of Joomla WITHOUT the subfolder installations?

The concept of JMS is to share the joomla installation (PHP code).
You can share the PHP code by different method that I will illustrate with cPanel admin tool.
- Park domain that allow sharing a same website between several domaiin that are parked in the same directory
- Add On domain where you can specify the same document root for several domain
- Symbolic Link that is a feature recommended by JMS when it is available because you can have different document root directory and in the same time share the joomla installation except few directories like the /images and the /tempaltes directory.

I suggest that you have a look in the tutorial video 0.a that present the concept and the video CP-04 that show a case with a subdomain.
www.jms2win.com/en/tutorial#jms12x-0a
www.jms2win.com/en/tutorial#jms12x-CP-04