What is Peter's rule in neuroscience?
I think that your interpretation is correct, although Principles of Neural Science (Kandel et al.) doesn't mention Peter's rule (which is where I would have hoped to find a simple explanation).

According to Binzegger et al. (2004), the idea behind Peter's rule dates back to Peters and Feldman (1976) and Peters and Payne (1993), though the Rule per se may have been coined by Braitenberg and Schultz (1991; at which point it was still called Peters' rule). Binzegger et al. describe it as:


  They assumed that axons simply connect in direct proportion to the
  occurrence of all synaptic targets in the neuropil. The rule can be
  extended to provide more precise estimates by taking into account the
  detailed morphometrics of the dendritic and axonal trees of the
  different neuronal types.


To paraphrase Binzegger et al., in the simplest form of Peter's rule, the number of synapses in a cortical layer are evenly distributed across the potential target neurons. So there would be a direct proportionality between synapses and targets.

The second sentence of the quote above is the meat of the Binzegger paper. They also present a mathematical model of a more complex and realistic variation of Peter's rule which takes into account different types of postsynaptic neurons and the fact that not all cells receive synapses.

Braitenberg V, Schüz A (1991) Peters' Rule and White's Exceptions. In: Anatomy of the Cortex, pp 109–112. Berlin: Springer.

Peters A, Feldman ML (1976) The projection of the lateral geniculate nucleus to area 17 of the rat cerebral cortex. I. General description. J Neurocytol 5:63–84.

Peters A, Payne BR (1993) Numerical relationships between geniculocortical afferents and pyramidal cell modules in cat primary visual cortex. Cereb Cortex 3:69–78.