How can I keep iCal from stealing/short-circuiting email invitations?
Your hypothesis is very close to reality: it seems (based on ArsTechnica article) that the default settings in Apple's iCloud calendar service automatically push calendar alerts to Apple iOS and macOS users and bypass e-mail entirely.

The same article describes how to change the settings.


  Visit your iCloud account via a Web browser. Log in to iCloud and go to the Calendar Web app, click on the Settings gear icon in the bottom left corner of the Calendar view, and click Preferences. Click the "Advanced" button in the Preferences pop-up window. At the bottom of the window, change the Invitations setting for "Receive event invitations as:" from "In-app notifications" to "Email to [your iCloud account address]."