I've never seen anyone use false negatives to argue that we should accept false positives as reasonable. I guess there's a first time for everything.

But to answer your question, yes, it would be statistically prudent to assume that everyone who passed your test is free of covid because the proportion of the general population who have it is less than 1% currently and your test produces a 100% positive rate.

This is a specific case of https://en.wikipedia.org/wiki/Prosecutor%27s_fallacy