You can choose to make auto-populated answers (e.g. First Name, Last Name, Email Address) non editable for the survey responder.
If they then forwarded an RSVP survey to someone not invited to the event, their details would remain in there, so the new person would not be able to RSVP with their details.
On a Free Text question, click Settings > Show > Auto Populate With (First Name, Last Name, Email Address etc.) > tick Non-editable.