Hi Katandmouse,
No collecting email addresses is not required to be able to edit responses, but the individual submitting the form does need to save the link to their response at the time of submission. This is created after submission by clicking on the "Edit your response" link - see below.
That link can then be used to edit your response immediately, or at a later time, if the form still permits it.

If you had collected email addresses, then you do have the extra option of sending responders a confirmation email of their responses, and this includes the link to edit their response, if you've enabled that. See below:
To maintain the anonymity features of Google Forms, there can't be any way for you to identify the responder from the spreadsheet end, unless they had agreed to submitting their email address, so there is no way (that I know of) from your end to give them the link to their response after the fact.
In the scenario where you are NOT collecting email addresses, it certainly could be clearer to the respondents that they need to save the link immediately, if they want the option to edit their response at some point in the future. To submit this as an enhancement request, use the Help - Help Sheets improve menu option, to sirect your feedback to Google designers.
I hope this helps.
Cheers,
Gill
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