We would like to publish Adobe Presenter Presentations to our website and provide URLs to permit certain people access to eLearning. We have been told that we do not need to publish to an LMS to do this. Is that correct? We realize that an LMS would provide us with more robust data and record management capabilities, but we are willing to forego that for the present. Will people be able to access and take the eLearning by our hosting via our webserver?
It is correct. You can indeed host the published output of Presenter on a simple web server. Any person with access to the URL will then be able to consume the content hosted.
Some additional information that you may find useful.
If you are using Presenter 10 or Presenter 11, you would be able to publish the output as SWF only, HTML only or SWF+HTML. If you publish as SWF only, the content can be consumed on desktop browsers with Flash plugin. If you publish it as HTML, the content can be consumed on browsers where Flash plugin is not available (including Chrome on Android tablets, and Safari on IPads). If you publish as both, there is detection logic built in to choose Flash wherever possible and fall back to HTML otherwise.