If you browse through your smart TV, and the smart TV overlays an ad over the browser window, or to the side, is that the same as saying the original server is serving those ads? I hope you agree it is not.
If you use a web browser from a phone vendor who has a special Chromium build which inserts ads client-side in the browser, do you say that the server is serving those ads? Do you know that absolutely no browser vendors, including for low-cost phones, do this?
If your ISP requires you configure your browser to use their proxy service, and that proxy service can insert ads, do you say that the server is serving those ads? Are you absolutely sure no ISPs have this requirement?
If you use a service where you can email it a URL and it emails you the PDF of the web site, with some advertising at the bottom of each page, do you say the original server is really the one serving those ads?
If you read my web site though archive.org, and archive.org has its "please donate to us" ad, do you really say that my site is serving those ads?
Is there any web site which you can guarantee it's impossible for any possible user, no matter the hardware or connection, to see ads which did not come from the original server as long as the server has TLS? I find that impossible to believe.
I therefore conclude that your interpretation is meaningless.
> "as shown in someones browser"
Which is different than being served by the server, as I believe I have sufficiently demonstrated.
> But don't be surprised when it happens anyway
Jason Scott, who runs that site, will not be surprised.