Earlier quoted context omitted.
> there is no way the website can detect that situation Why? The website can salt, hash, match your password against all the hashed passwords for all the closest usernames within a certain edit distance. Not saying this is a good idea security-wise, but it's not impossible.
Apart from the security issues you've yourself noted, it's possible that the entered password matches another account's password coincidentally, not because the user intended to log in to that account.
This is not a very big problem security-wise. It makes online attacks slightly easier, but you can limit online attempts pretty easily. It doesn't affect offline attempts at all.
The downvotes dheera got are extra inappropriate because they were just saying it's doable.