As I tried to explain: no. This is not the only possible cause.

a) The version of FF on your desktop and on the tablet are not the same, and the UA-string the browser sends isn't.
b) The operating system isn't the same, even if you would be using a desktop based on a Linux kernel.

So if Apple returned to its habit of delivering different versions of their site for different browser/OS combinations (and maybe even blocking unknown browsers), the HTML your desktop browser receives might be completely different from what the tablet's browser gets.

This is not an assumption, actually I have no reason but my past experience with Apple to come up with this. It's just to point out that it's not necessarily the browser's fault if a certain site doesn't work when it works on another PC.