My memory is too bad to remember the exact timings, which I suppose make a difference in this. Did she make up the Asian grocer lie while there was still a chance that they could survive? From my recollection it was known by the time she was interviewed on August the 5th when DC was well known, and she definitely previously mentioned Woolworths to the doctors when they were in hospital. However, I can't remember exactly when it first came up.
I suspect she first used the excuse after the mushrooms were already known to be the issue, and maybe even after DC had been mentioned. At this point, she is simply trying to save her own bacon and has come up with a very poor excuse for the presence of DC. She clearly thought they'd think that anything could come from an Asian grocer so this was the probable origin.
If it was prior to her knowing they suspected the mushrooms and they were just trying to find the possible source, then I suspect your idea might have some merit.