The message is correct!
In Windows, every user account is globally unique, meaning no two user accounts can ever be the same. Thus, 'you' on your old computer is not the same as 'you' on your new computer. Even though they are both 'you'.
Now you understand why 'you' on your new computer can't copy a directory from somebody else's old computer - even though that somebody else is still you.
The easy way around this is to copy the folder to an external hard drive or a USB flash drive, and then move the folder to your new computer. The copied directory inherits the permissions of the root of the external hard drive or USB flash drive, thus breaking the link to the old computer.