"Note that there are two way to interpret this result:

The speed of light was constant with respect to the aether. This theory turned out to be false. Read more about the Luminiferous aether.

The theory of Relativity"

The most they say is just the assertion: "Maxwell's equations are Lorentz invariant"

Before the Michelson-Morley experiment 'disproved' it, it was assumed that the waves propagated through the 'aether', and that c was therefore the speed relative to the aether. So, in addition to Maxwell's equations, extra experimental data was needed.