Webform Submission URL Access Control
I think you need to grant the Webform: Edit own content permission. This may still not give access to view the submission (haven't tried) but it would give the user access to edit their submission, which is probably more important (tweak the link you email out to edit rather than view the submission).

If all you want is to allow the user to see their submitted values, I second Karin's suggestion that you put them in the body of the email. This way the user can see them immediately without needing to click on a link.