Mark,

I've lived some hundred yards from Switzerland for about 15 years (with better access to Swiss TV, so I know what you mean. The speakers of that Alemanic dialect prefer to call Swiss-German a language and to use the word 'dialect(s)' for Berner Deutsch, Glarner Deutsch, Zurich Deutsch etc.

But that does not mean much, for those Germans who speak the Alemanic dialect (in the very South West of Germany) and those French who also speak the Alemanic dialect (Alsatians) also would name their dialect a language (sprooch).

Less seriously, as long as the Swiss German speakers themselves name the language Schwyzerdütsch it still is a dialect of German. And it can never become an own language for purely geographical reasons: "A language is a dialect with a navy".

Paul,
no, I don't think she would have been glad with that

Swiss German is actually at the brink to a new language for several reasons in my layperson eyes.
It not only has many completely different words (East-German and West-German also had about 500 different words after a separate history of only 40 odd years).
It has a completely different grammar and the stresses are often completely different.

More reasons for it being a language already:
(1) A Swiss German speaker is unable to speak more or less of his dialect. There is no real continuum between a broad dialect and Hochdeutsch. She either speaks Hochdeutsch (with a dialect sound which most Germans wrongly consider to be Swiss German already) or she speaks real Swiss German (that by foreign speakers of German often is not even recognised to be a variant of German).

A teacher would use Hochdeutsch in her lessons and might switch completely to Schwyzerdütsch for a personal remark (Pirmin, could you pay a bit more of attention, for instance.

When I watched skiing in Swiss TV, the speakers always would use Hochdeutsch until the moment they did an interview with a Swiss skier. So without any warning he would start the next sentence for instance like this (I transcribe it how it sounds to me):
Und nu hämmer bi üs d'Marie-Thräs Nadig. Marie-Thräs, wie isch's hüetige Ranne g'si.

(2) There is a third hilarious variant of Swiss High German which also demonstrates that the dialect might soon be a language. In private TV and radio in Switzerland the language used is often Swiss German throughout. And then comes the moment when the speaker reads a news item. The news item has been written in Hochdeutsch and he reads it in Swiss German. That sounds awfully wrong like a nonexisting dialect, for the grammar and the order of words are completely Hochdeutsch and the words and the pronounciation are Swiss German.

Wolfgang