yeah I know, the only reason I mentioned the incognito is that you said "I tested it and it works ok". that's because of a cookie that was already created. if that cookie reaches the Max-Age, and you use the edit-order direct link, It will ask for a username and password.
To understand this better, It doesn't ask me to log in when I'm in incognito mode and go to "Catalog > Prestools Suite". (It never asks for a username and password when I open the script this way). But if I close the incognito and reopen it, and then log in to BO and that order link, It will ask me to log in.