I agree with Hadley's original assessment, in that case. It sounds like your students are using the following workflow:
- Clicking the "Knit" button
- Then clicking on the "Open in Browser" button when the preview comes up
- Finally, saving the web page using their browser
In reality, the HTML file was already made in step #1, so it's not necessary to "Save" the knitted file after that. Are they using RStudio desktop or server? In the case of the latter, it may be that they aren't realizing that they can download the HTML file from the server. If it's the desktop version, they just might not know that there is now an HTML file in the directory with their Rmd file.