Even today, there exists no consensus about which is the correct expression for the electromagnetic force. Most people are happy to use approximate expressions that are known to be valid only in restricted circumstances (like when the forces are caused by interactions with closed currents, or the forces are between stationary charges).
Moreover, when the vacuum equations are written in the simplified form present in most manuals, it is impossible to deduce how they should be applied to systems in motion, without adding extra assumptions, which usually are not listed together with the simple form of the equations (e.g. the curl and the divergence are written as depending on a system of coordinates, so it is not obvious how these coordinates can be defined, i.e. to which bodies they are attached).
While the vacuum equations are fundamental, they may be used as such only in few applications like quantum mechanics, where much more is needed beyond them.
In all practical applications of the Maxwell equations you must use the approximation of continuous media that can be characterized by averaged physical quantities that describe the free and bound carriers of electric charge. The useful form of the Maxwell equations is that complete with electric polarization, magnetization, electric current of the free carriers and electric charge of the free carriers. It is trivial to set all those quantities to zero, to retrieve the vacuum form of the equations.