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Looking at the review queue, I just happened to tap on one of the user's avatars in the list of recent reviewers:
After tapping on it, I came to the profile:
Wait... 419 rep? The user is 1581 reputation away from being able to get in! How did this happen?
I too was in this situation once: my first Custodian badge was awarded for reviewing a suggested edit when I had just over 200 reputation.
This is possible if someone with under 2,000 reputation edits a post of yours, you get notified to review it (note: users with 2,000 or more reputation can bypass this as they do not need their edits reviewed). This happens regardless of how much reputation you have, and it's nice that you as the author of the question are allowed to review such edits in case they're invalid.
I believe this is the only review type a user can participate in (albeit in a very limited way) without first requiring a certain amount of reputation.
Look at every single one of the user's suggested edit reviews. They are all on his own posts!
The user probably went to one of his own posts and saw edit (1), and clicked it out of curiosity. They were then presented with the typical review pane.
It seems that even the users with <2K can review edits on their own posts.
