Welcome to the forum.
I just answered your question on Linked In.
For the benefit of followers of this forum, here is my answer.
If I read you correctly, the users would be viewing the help, decide a change is needed and make it from within the browser, subject to being able to enter validation credentials.
Ignoring the need for the browser to have an add-on that supports that, I don't believe any HAT would enable would work that way as the source files are not the same files as the output files. Thus even if I edited and output file, next time someone with the source files publishes a change, my change would be lost. Their starting point would not be my update version.
With HTML editors such as Dreamweaver, source files are published to the server without change. There are tools that allow changes to be made to what is on the server subject to the user being authorised. However, you still have the same issue when the source controller makes changes. At least here though, they can pull the published file back to their source. Additionally tools such as Dreamweaver don't support single sourcing in the same way as a HAT, they don't have build tags and so on.
Anything that allows a number of people to make changes direct to what is on the server is going to have a management overhead.
One solution would be using a HAT such as RoboHelp with source control. Then those authorised to make changes would make them to the source and publish. That does of course mean all these people have to be trained in the use of the HAT and have valid licences, always for the same version.
I have seen customers ask for the ability to have authorised users modify our help files. When we explain what their staff will need to do and the problems when we update the source, it's amazing how the "must have" requirement becomes an "oh, we just thought it would be useful" requirement.
Maybe commenting would be a solution. RoboHelp produces AIR Help which is installed locally and allows users to make comments on topics. These are saved locally but can be shared between users and the comments will survive an update to the help. If a web based output is a must, I believe there are tools that do the same job. The problems arise when it is the help topic that must be edited.
This link is out of date as far as mentioning commenting is concerned but nonetheless might give you some useful information.
See www.grainge.org for RoboHelp and Authoring tips