From Redditor Decolater's summary:

...So the Governor is told by the DEQ - their agency responsible for public safety and drinking water - that the water is safe. This is July 24th.

In the wake of Muchmore’s July email to Department of Health and Human Services Director Nick Lyon, follow-up communications reveal health officials attempting to analyze the latest testing results and set up a public information program for Flint residents. They also show health and environmental quality staffers struggling to interpret data that showed elevated levels of lead in children’s blood during the summer months. ("Flint crisis response delayed for months")

Remember hindsight. It's easy to to judge others after the fact. Was what was known at the time enough to state with certanty that there was a lead problem with the water? The two departments responsible for public safety, the DEQ and the DHHS, were gathering data. It sounds easy from your armchair perspective, but from a scientist - which these guys and gals are - you state what the data shows you based on the methodology you are required to use.

Look at how the Detroit Free Press describes the DHHS analysis of the data:

But the analysis of children's blood-lead levels the health department relied on to ease chief of staff Dennis Muchmore's fears was just one of two performed after his e-mail. Another analysis, done by a health department epidemiologist, showed the reverse: "There appears to be a higher proportion of first-time (elevated blood-lead levels)," the epidemiologist wrote, in a report also obtained by Edwards. "... Even compared to the previous three years, the proportion ... is highest in summer ... positive results for elevated blood-lead levels were higher than usual for children under age 16 living in the City of Flint during the months of July, August and September 2014." ("In Flint, report that raised flags on lead went ignored")

That sounds pretty damning. However, we have this conundrum as scientists. We need to look at data from all sides. Here is what the DHHS understood about lead levels in their citizens:

Lead levels tend to rise annually at that time of year, and state researchers grappled with determining whether the 2015 increase was typical or beyond the norm. ("Flint crisis response delayed for months")

The Detroit Free Press acknowledges this "grappling" but downplays it as if it can be ignored:

The epidemiologist's analysis, the one that showed a spike in kids' blood-lead level in the summer of 2014, never made it out of the department, a spokeswoman said. ...it wasn't clear that the three months' worth of testing analyzed were statistically significant. At the end of the summer, blood-lead levels dropped, so the epidemiologist had just three of the five data points Wells said are required to show significance. (For what it's worth, this argument didn't hold much weight with the Free Press' data analyst, who teaches graduate-level statistics.) {source}

...For a good time line up to June 2015, read the EPA memo.

(I didn't see a copy of the analysis, but dollars to donuts it found an extra-seasonal rise but p>0.05.) From WP:

Volunteer teams led by Edwards found that at least a quarter of Flint households have levels of lead above the federal level of 15 parts per billion (ppb) and that in some homes, lead levels were at 13,200 ppb.[25] Edwards said: "It was the injustice of it all and that the very agencies that are paid to protect these residents from lead in water, knew or should've known after June at the very very latest of this year, that federal law was not being followed in Flint, and that these children and residents were not being protected. And the extent to which they went to cover this up exposes a new level of arrogance and uncaring that I have never encountered."[25] Research done after the switch to the Flint River source found that the proportion of children with elevated blood-lead levels (above five micrograms per deciliter, or 5 × 10–6 grams per 100 milliliters of blood) rose from 2.1% to 4%, and in some areas to as much as 6.3%.[4]...On January 18, the United Way of Genesee County estimated 6,000-12,000 children have been exposed to lead poisoning and kicked off a fundraising campaign to raise $100 million over a 10-15 year span for their medical treatment.[2]

This translates directly into a decision problem with Expected Value of Sample Information (possibly a POMDP): the harms of lead are well known and very high, the water levels affect a lot of people, the cost of remediation strategies is probably known, and the cost of taking additional samples of various kinds also well known.