Reality is more complicated than that. Grandparent is right about deaths from fire in many parts of the world. The following deals with the fire death rate from 1979 to 1992.

The U.S. fire death rate fell 46.3 percent, from 36.3 fire deaths per million population in 1979 to 19.5 fire deaths per million population in 1992. As shown in Figure 2, however, this trend was not limited to the United States; rather it was international. Of the countries considered, only Hungary and Denmark recorded increases in their rates of fire deaths over that period – all the other countries lowered their fire death rates. The reduction in fire deaths for the United States (46 percent, or 16.8 fire deaths per million population) was the largest absolute and relative drop of any of the countries shown – almost twice the size of the next biggest drop (the United Kingdom, with a reduction of 38 percent, or 9.0 fire deaths per million population).

-- "Fire Death Rate Trends: An International Perspective"

For the US in particular, this trend has continued into the present.

We leave as an exercise to the reader what exactly the flaw in your argument was.