The fact that you also triggered a War at the same time is coincidental and just a result of the Influence changes that came with the positive economic actions. I think War would happily stack with Famine if you weren't simultaneously trying to increase the Economy slider.
Pretty sure you're wrong here - when the WAR traiggers I lost the FAMINE, went back to NONE. Then it starts reqaquiring the BUST (the dot is still in the FAMINE section, if you were correct I think it would have restarted acquiring the FAMINE). I'm sure if they hadn't broken the BGS it would have continued and once I had the BUST it would have gone on to reacquire the FAMINE, but it does seem that if you block a FAMINE with a WAR then the BGS will go back through NONE -> BUST -> FAMINE.
ofc this is all moot, as the currently broken BGS and the tendency for the BGS to return to the mean without external influences (influences which are blocked by the broken BGS) means that the dot in my system is now in BUST, and I really don't know if I can be bothered to do this again.
Sadly this means I don't really have the data to bug report this, so someone else can have the honour when they hit it in a few months time.