Indeed; so when the second was defined by a fraction of a day, that day was an abstraction which approximates any given synodic day. I take your point that the author's quoted statement was incorrect, as the synodic day is a function of the earth's orbital period as well as its rotational one.

I also take your point that we don't care about a specific transition of a cesium atom per se, but I am not so sure that any more than a rather small fraction of the population care that a second is 86400 of what was an average day at some point in time (even though it is is a good approximation for today's days.) What fraction, I wonder, have ever performed a calculation on seconds using that number, other than, perhaps, for pedagogical purposes? Other than that, is it not just a convenient short interval where its constancy (a property that cesium delivers better than does the Earth's motions) is paramount? One might point out that such calculations are frequently done on their behalf, but from that perspective, the recent large increase in the use of GPS, with its heavy computational demand that is dependent on the constancy of atomic clocks, should equally be taken into account.