Looking at that graph, I think I have an idea about what happened. The first deaths were in people with underlying conditions because the virus killed them faster than the "healthy" group. Since the number of cases is growing exponentially, there are still a lot more people dying with underlying conditions, but for every one of those deaths, there are maybe 2-3 "healthy" people still sitting in the ICU whose prognosis is grim.
The problem is that to establish a true CFR, you need to randomly look at the outcome of a large number of cases. Say we pick 1000 people who were confirmed to have the virus in early May. By May 15, 3 had died and they respectively had cancer, AIDS, and Asthma. At that point, it is fair to say that people with health conditions are at highest risk, but of the 1000 cases, 47 are still in hospital while 950 have recovered. By June 1, there have been 3 more deaths and two of them have underlying conditions, while 25 of the hospitalized cases have recovered. By June 15, 3 more deaths and none of those had underlying conditions, while 10 recovered. Buy June 30, 5 more deaths, all healthy people while 1 recovers.
In this scenario, 5 deaths per thousand had underlying conditions while 9 deaths per thousand were healthy and when compared to the overall population in which a third of people have underlying health conditions there is no significant correlation.
By the end of June there are so many new cases due to exponential growth where the people dying have underlying conditions that the healthy deaths don't show up in the stats.
But because it takes longer for the healthy people to die and for the results of the CFR study to be tallied, public health people don't have studies to go by and just look at the deaths vs. cases numbers and come up with the underlying conditions statements.