I believe that idea is pure bunk. The only way I can think of for a small component to build up to a disproportionately large result over time, while the Moon's result stays about the same, would be for the small one to hit some sort of a resonance with the body of our planet. The trouble with that is that it should level off asymptotically at a low level because of damping in a rather short time.

For a rough analogy, suppose I sit in a rocking chair and bob my head gently at the resonant frequency. The oscillations will increase in amplitude for a short time and then level off if I keep the impetus at a constant value. On the other hand I can tip the chair over by making a sufficiently violent motion, even if it is nowhere near the resonant frequency.

Suppose for the sake of argument that Pluto, or any planet for that matter, does cause a resonant oscillation that somehow does not get damped and continues to grow. If it did get large enough to offset the normal tendency for tides to be highest with the Moon near perigee at spring tide, those who keep track of the tides should have seen it right away.

If Robert Tulip cannot come up with a better theory than that, I have no choice but to dismiss the apparent planetary effects as statistical flukes, which can and do happen. For example, variable star observers have looked for possible periodic components in the irregularities of the pulsations of Mira and similar stars. Sometimes they would see something that looked roughly periodic over a couple of decades, but when they tried to extrapolate the resulting empirical formula it fell apart. I am going to search for the Sky and Telescope article where I read about it. It was about 30 years ago so this may take a while.