Well, essentially, almost everything is stated correctly except for one point which I will elaborate on below. So, two independent but mutually influencing ratings are under consideration.
Of course, one could try to argue about the decay by taking an average between 1/3 and 1/10. It will be slightly harder to calculate, but it's essentially the same as 1/3.
And another thing, why do you say that some random player will break ahead if the rating leader misses a couple of Tournaments? The one who was nipping at their heels will move forward. This will happen regardless of the decay value. Seems like no one else is talking. It's not because the system has become so complex that people no longer get it or don't want to get it :)