Of course the person may have multiple user accounts and he may have given the "wrong" password for the "right" username account, but he may also have given the "right" password for the "wrong" username.
You could provide the correct password to your account 'test', but not 'ttest'.
The server just tells you to check both instead, it's more semantically correct and offers some security improvements with user enumeration.
Imagine both 'dave' and 'davr' have an account. I'm 'dave', but I accidentally type 'davr' and my correct password. Now the site will tell me that my password is wrong. So I retype and retype my password over and over again and still can't log in, because the problem isn't the password like the error message says, but rather that I typed the wrong my username.