I think you two are talking around each other. In most cycling conversation, the "elevation" or "elevation gain" of a ride usually refers to the cumulative elevation gained while traveling on positive gradients, not the elevation difference between the start and finish of a ride. The former is path-dependent and is comparable to a shoreline problem*, the latter is not.

*Or at least, it's comparable on a hypothetical level. For practical purposes, riding reasonable paved roads on a road bike is usually a smooth-enough situation that the minimum-ruler-length-that-it-makes-sense-to-use isn't that fuzzy of an issue.