There may or may not be an increase of cases when the economy opens. While the former is more likely the latter is not out of the question, depending on whether the community will take precautions like wearing masks.
However, if the economy stays closed, without a doubt, many lives will be negatively affected.
Why did you ignore the line right after the statement you quoted? What we've seen over and over in each wave of the coronavirus is that the deaths lag behind the number of cases by a few weeks [1]. What you're arguing for is irrational and against the facts of the situation because the reason why we've seen an increase in cases is because our state opened up too early and too recklessly!
How can you honestly argue that there won't be an increase of cases when the economy opens when we're facing down exactly that situation?
[1] https://www.businessinsider.com/coronavirus-deaths-can-still...