I was able to get my inaccessible account merged into my active account despite the incongruity of the language on that page, and despite not being able to comply with the request to edit the inaccessible account's profile.
Regaining access to the lost account was not necessary; instead, I was able to provide proof to SE support, via email, that I was the rightful owner of that account.
I believe the wording of that page should be amended so that it is not instructing the user to perform an impossible feat. If you've lost access to the account, as indicated by clicking that link, there is no possible way to adhere to the instructions that follow by editing the account's profile.