Source code implies it's a programming language. This is not. This is HTML, which is a Markup Language (hence the ML in HTML).
There is probably some Javascript code there further down but you didn't look at it.
In common parlance, Twitter's source code is the source code to their web services and backend systems, which is not public.
Are we going to giggle about how those dumb browser developers don't know that it's not actually the application server source code, or can we admit it's the source code of the rendered page, a different layer of the stack?
Is it really that much of a mistake to shorten "Twitter's [html] source code"?
Frankly, I think a bigger pedant could come in here and correct you.
Check out Alan Blackwell's "What is programming" paper from 2002. In it, he argues that we should not be asking "is writing html programming", because that question comes from an older (past overdue for revision) mental model of what programming is all about.
I can't recall ever seeing someone use the phrase "X's source code" to mean HTML. In my view it's data, not code. Just like you wouldn't call some XML file "source code" -- it's purely descriptive markup. When a browser's context menu says View Source, the word "code" isn't implied. It's the same usage of the word "source" meaning "origin" (as in "cite your sources").
Maybe I'm being overly pedantic, but the phrasing definitely read strangely to me regardless. Speaking as someone who's done a mixture of programming and web development for over two decades.
That would make me wonder about the interviewer's experience. That's not a feeling you want to have at the start of an interview