What you describe is in a broad sense true, and also why it is difficult for a planetary system to become stable. But when there are resonant orbits (1:2, 1:3...ratios) the minor perturbations of other planets are self correcting: if the smaller body gets 'ahead' on one orbit, it will be pulled back. If it gets behind, it will be pulled ahead on the next pass. The establishment of resonance has an overall stabilizing effect; and this is why the resonance between Saturn and Jupiter is so important.
“It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.” ― Arthur Conan Doyle, Sherlock Holmes