There's a difference between selecting a file and choosing File→Open With..., and selecting the same file, choosing "Get Info", and making a selection from the "Open with:" menu. Yeah, yeah, they're both "Open with..." menus, but they're different "Open with..." menus.
The former means "Open this file, but this one time only open it with the application I select". The file is not modified, and will open next time just like it always has.
The latter means "Change this file so that it always opens with this application, irrespective of how it behaved before, or how similar documents behave." (What happens is that an alias to the application is stored in the resource fork of the file, creating that resource fork if needed. The application is also asked what icon it would normally assign to this type of file, and the file is given a matching custom icon, also stored in the resource fork. For completeness, a copy of the appropriate "kind" string is also copied into the resource fork, where you'll see it after "Kind:" the next time you Get Info. Naturally, you need write access to the file to pull any this off.)
Unless, after making a selection from "Open with:" in the Get Info dialog, you click on "Change All...". In that case, the document is not altered. Instead, your personal copy of the Launch Services database is updated to say that all similar documents should open with that application, when you're the one doing the opening. (With any luck, this document will be similar enough to itself to be affected.)
In case of a conflict, "Get Info→Open with" trumps "Get Info→Open with→Change All". That is, if you've specified what application opens this document, it doesn't matter what application you've selected to open similar documents.
If you try to change the "Open with:" attribute of a file you don't have write access to, you'll be asked if you really wanted to "Change All..", since that's the only kind of change you can make.
Aliases have nothing to do with it. The alias leads to a document, and it's the document that decides (with help from Launch Services) how it's going to open.
And I emphasize: Finder's File→Open With... menu command is a "just this one time" deal. Neither the file nor Launch Services nor any aliases created before or after are affected in any way. It makes up for its lack of permanence by being able to override any other choice of application.
