I'm guessing it's more to do with the interaction of the gravitational vectors of sun and moon. During a half-moon it is pulling at a right angle to the sun, during a new-moon with the sun, and during a full-moon against the sun.

Probably the same cause of tide supercycles - when moon and sun line up, the pull is additive. When they oppose, the moon detracts from the sun’s pull by a bit.

Writing that out I’m not sure it makes sense, but someone smarter will be along to correct me shortly.

When the moon is full it is opposite the sun and reduces the effect of the sun’s gravity. When it is new it is in the same direction as the sun and increases the pull toward the sun.

I guess they probably meant moon position in orbit, in general