It's a lie because the URL being displayed does not reflect the source of the bits.
> If I'm offline and I open an offline cached page in my browser, would you call it a lie if the browser displays the URL I originally downloaded that page from
That's a bit of a gray area. Yes, it is a lie (the browser should provide an indication of the actual source of the bits). On the other hand, the cache was created by you and exists on your own machine, so it's more of a little white lie in that case.
It's a lie because the URL being displayed does not reflect the source of the bits.
> If I'm offline and I open an offline cached page in my browser, would you call it a lie if the browser displays the URL I originally downloaded that page from
That's a bit of a gray area. Yes, it is a lie (the browser should provide an indication of the actual source of the bits). On the other hand, the cache was created by you and exists on your own machine, so it's more of a little white lie in that case.