You're missing something.

Imagine it like this. You have a file. You have a "database" which, when you try to access that file, your system goes to the database and says "where is it?"

If you hardlink, then when you try to access the file in location a, the database says "it's in location a" and when you try to access the file in location b, the database says "it's in location a".

If you delete it from location a, then the database removes its first entry, and updates its second entry to "it's in location b". If you delete it from location b, then the database removes it's second entry.

Does that make more sense?

To your system, to you, to everything that matters, there are TWO FILES and they are completely independent. Rename them, move them, delete them, whatever. If it can't maintain the hardlink, then it just removes or updates that hardlink. The hardlinks are pointers only.