If that were true, there would be a lot more websites showing this issue and a lot more people reporting it. Everything points to an issue with the specific website.
Since you mention that the owners wouldn't understand this issue, I'm guessing they didn't build the website by themselves, and instead are using some third party hosting. Often times, these services use needlessly strict security rules, such as restricting access to less common user agents:
You can use an extension to change your browser's user-agent so that your Linux machine shows up as Windows to the eyes of the web server.