Does everything produced by The LEGO Group count as "LEGO pieces"?
There is no official answer on this, as “purist” LEGO is a consensus, not a definition. That said, there are several examples of pieces LEGO doesn’t classify as a part that are used in MOCs, such as:


The pin used to keep bundles of 4 train tracks together.





This Technic hub piece was never originally intended for standalone use (it was part of a pin joiner) but has been used by MOCcers due to having antistuds on both sides (within a 1x1 brick footprint). It was later used as a standalone piece in official sets before being replaced with a new design.





The iconic brick separator is not intended as a regular LEGO piece, but has a whole class of MOCs based on it. I have seen it used as railway station roofs, spaceship wings etc.




Net, I think the general consensus is that if it has been produced by LEGO and you can find a way to incorporate it into a MOC, your creation is still considered “purist”. At the least it gives you good arguments for any debate that might arise. 

Curious to see how you will incorporate shopping bags in a MOC ... I can imagine one being used in a rather large scale MOC where you utilize the LEGO logo on it as part of a display.