Yes I had the same issue. But the wording "there is a < 5% probability that an outcome was the result of chance" is in fact problematic since many readers will go on to conclude "hence a >95% probability that the outcome was not the result of chance", so it is easier to misinterpret than the technical definition P( Observation | H_0 ).

In courses I will typically use wordings like "If there was truly no association, then the probability of getting an observation like this is <5%".