Looks like you guys were right and I was very fortunate all along - I stand corrected and apologise if anyone was misled. I took it upon myself to verify it from SBB:
Thank you for your query. (n° CC5990937)
Your GA is only valid from Schaffhausen to Erzingen , if you take the train through Germany. In this case you need a valid ticket.
If you travel trough Switzerland your GA is valid.
I've just received a contradictory but favourable response from SBB. So I'll just get a new GA card and keep a copy of SBB's response with the GA card.
I think most DB ticket inspectors won't care what SBB say about DB trains, however, if it contradicts their own management. I'd try and get a letter off DB if I were you to be safe.
I commuted from Basel (Gundeli) to Schaffhausen with the DB Bahn for ten months. That was as long as I had energy to keep it up. Waking up at 5.30 to catch the train around six and then, in best case, take the train at five back and be home at seven. I have to be honest, it's very heavy on you, on your partner and do not forget the social life which you won't have anymore. The more demanding job the harder it is.
I bought a monthly card at DB for around 110 EUR for a month, I could use it for the trams in Basel as well. The GA was not valid and no commuters in the crowd had it.
The positive thing with going with db is that it's a direct train without any transfers; meaning one hour to do what ever you want without any stress of changing trains. For me it meant SLEEPING which was very much needed after a hard day of work and waking up early. However, that sleep didn't prevent me from being exhausted when coming home.. I recommend you to think it over...