Actually, the dustbags that come with most of the authentic bags have white drawstrings, not purple thick ones, as mentioned by Mamamaxim above. Also, I have a beige colored SM bag that I purchased at Bergdorfs and the fabric is a bit lighter weight and rather flimsy/slouchy compared to other SM bags.
I'll agree with this--I have many stellas and all were purchased at department stores...every dustbag has a white/beige drawstring. Personally, I've never seen a purple one (not saying those don't exist, just that none of mine have that color).