Actually, the comma is pretty insignificant with respect to the central issue of different views and debates about the nature of "grammar". The sentence is typical of an example of an ambiguous one which demonstrates the difference between deep structure
and surface structure
in Chomsky's "Transformational Grammar". Other celebrated Chomskyan examples (which generally imply speech rather than text), are...
Flying planes can be dangerous.
Visiting relatives can be a bore
Ambiguity is accounted for by two or more deep structures mapping to the same surface structure.
Alternatives to traditional grammar, and transformational grammar, include "discourse analysis" which transcends "the sentence" as a unit of analysis, thereby resolving ambiguities.
Setanta's point about a joke is valid insofar that most, if not all, linguistic jokes might be said to involve sudden awareness of a shift in "deep structure".