Is there a way to notify just a particular person when a smart group membership changes?

What we do is that we have special accounts without any real access and these accounts are assigned the emails. You can configure each account to have different preferences if they want notifications on smart groups or policy errors and whatnots.
Results of a search can be exported to CSV, HTML and so on, look all the way down on a results page.

Or, I may have misunderstood the question?

The email on group change function doesn't email the owners of the Macs. It emails anyone who has the specific privilege setting within their JSS account (local or from LDAP) to get notified of such Smart Group changes. Unfortunately, its not very granular. If the box is checked to send change notifications via email, anyone that has that setting enabled will be notified. You cant send it only to one group of people and not another, if all of them have that setting turned on.

As for pulling an inventory search and emailing it, as it turns out, I've been working on something that can do that, but it would not be something to run directly off your JSS, unless your JSS is hosted on a Mac server anyway. So in short, its possible to do it. But I'd really love to see auto email sending of reports automated by JAMF.
https://jamfnation.jamfsoftware.com/featureRequest.html?id=411

Thanks for the info guys. I didn't realize it was a specific preference for each JSS admin. Wish there was a bit more control over who to email. I upvoted the request.