Hi akwein ,
If you're OK with asking those respondents who want a response summary to enter their email address in a question, you could use the input from that field in an Action, and send them the summary after they Submit. Those who don't enter an email there would never receive the response summary.

Thanks MatthewM .
That's almost exactly what I need, except what I didn't mention is that this particular survey is set to NOT record survey responses. So as a result, I think it's behaving as if there's nothing to trigger the action--since the only options are response created or response updated.
I may be missing something though, since I'm new to Actions. Here's what I have set up:
Trigger based on event: Survey response created / Survey response updated
Condition: [email address field] is not empty
Action: Send email to [piped email address], send immediately, include response report and recipient data

I tried testing both options for the trigger separately, but no luck with either. I'm assuming "response created" means it was submitted to the database, rather than it was opened/started by the user.

Looks like you have it set up right. But I think you've identified the reason why it's not working. If Qualtrics isn't recording responses, then it wouldn't be able find an email address to send the response summary to. I'm not even sure it would be able to generate a response summary at all if you have it set not to record; you might try testing that out by removing the "[email address field] is not empty" condition.
Sorry, if not recording responses is a requirement, there may not be a way around this limitation with the built-in options in Qualtrics.

It does show the response summary (which has a download pdf link), but I think you're right that not recording responses is getting in the way of the email action.
I just chatted with support about what "response created" and "response updated" really mean. "Response created" means the participant opened and completed/recorded the survey. "Response updated" means that an already completed/recorded survey was edited using Qualtrics API. He confirmed that there's no way to use Actions as intended if the "do not record responses" option is checked.

Can we have this as a feature request please? I want the ability to set "do not record response after summary response have been emailed to the appropriate persons designated on the email tasks".
This feature is needed for me because I would like to create a form using Qualtrics to record data just enough so that it can send me the data as soon as the respondent completes it, but not enough so that the data gets recorded and client's sensitive info is stored into Qualtrics server. I want Qualtrics, the middle man, to hand over to me the sensitive information ASAP and then destroy any record of it. Manually deleting responses in real-time is not ideal.
Having this feature will help me secure user data so that it's only floating on Qualtrics server for as little time as possible.

Hi akwein
Sorry to jump in, but wouldn't a workflow be a solution? An email with a link to their responses can be sent after every submission.