Because the editor at /profile/edit/ only ever edits the account you are signed in with. If the username in the address is not yours, the page swaps in your own username and loads your editor instead. It does that in place, so the address bar quietly changes and the page looks like it ignored what you typed.
Nothing went wrong and nothing was refused. There is simply no address that opens somebody else's editor.
What each address does
- /profile/edit/ with no username. Signed in, you land on your own About page. Signed out, you go to sign in first and are returned here afterwards.
- /profile/edit/your-username/ Your editor, as expected.
- /profile/edit/someone-else/ The username is replaced with yours and your editor loads.
Because the swap replaces the entry in your browser history rather than adding to it, the back button will not take you to the address you typed.
To look at another member instead
Their public page is /profile/their-username/, with no edit in the middle. That is the page you reach from their name anywhere on UNI, and it shows their work, their About section and their links exactly as they wrote them.
If something on their page needs changing, only they can change it. Nobody else can edit another member's profile, whatever their membership.
Organizations work differently
An organization is not a member's profile. If you help run one, you manage it from that organization's own pages, not from anyone's profile editor, and what you can change there depends on your role in the organization.
If it is your account and it still redirects
Check the username in the address against the one on your profile. Changing your username changes the address of your editor as well, so a link you saved before a rename will now be treated as somebody else's and swapped.