Unless someone can show me otherwise, I don't believe a web client user can see the history "exactly" but they can see Revisions and Versions in the "Get Version" window and they can get latest version of a file if it is in a folder and state they have permissions to view.
The web client user can select a file, right click it, and click "Get Version" as shown below. Notice the warning the web client user sees if they do not have permissions to see any versions of a file or referenced file as shown in the bottom image.
Hope this helps you.
Thanks a lot, Tim. You answered my question.