Not exactly!
For one thing the latency is 6-24 hrs.
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Mushroom Poisoning
Poisonous mushrooms are eaten by mushroom hunters out of ignorance, after misidentification as edible mushrooms, or as a psychoactive drug. Mushroom poisoning commonly leads to consultation with a poison information center and to hospitalization.This ...www.ncbi.nlm.nih.gov
For another, death cap ingestion has not been confirmed as source of poisonings.
6-24h is still a pretty small window for them to all have been together eating or drinking something though.
Don't forget that EP is running with the mushroom theory herself by admitting they were in the meal including from a mystery store, so that is evidence also. Its not like she said, there were not mushrooms in the meal and has no idea what they are talking about. She actually confirmed the theory.