Why does the "DISPLAY OPTIONS" change?

I'm using a pure 7.x-3.1 version WITHOUT the recent patch → (#7) on a new installation of Drupal 7.50. Here's how to reproduce this problem:

1) Create a new template with at least one bundle selected.
2) Go back to edit this template. -> "DISPLAY OPTIONS" is empty.
3) Save this template with at least one bundle selected.
4) Go back to edit this template. -> "DISPLAY OPTIONS" is still empty.

I) Create a new template with NO bundle selected.
II) Go back to edit this template. -> "DISPLAY OPTIONS" is NOT empty.
III) Save this template with at least one bundle selected.
IV) Go back to edit this template. -> "DISPLAY OPTIONS" is STILL NOT empty.

A) Create a new template with at least one bundle selected.
B) Go back to edit this template. -> "DISPLAY OPTIONS" is empty.
C) Save this template with NO bundle selected.
D) Go back to edit this template. -> "DISPLAY OPTIONS" is NOT empty.
E) Save this template with at least one bundle selected.
F) Go back to edit this template. -> "DISPLAY OPTIONS" is STILL NOT empty.

When I say "DISPLAY OPTIONS" is empty, I mean to say that it looks like the one for the Flag Lists module WITHOUT the recent patch → (#7) that's trying to solve this problem.

And when I say "DISPLAY OPTIONS" is NOT empty, I mean to say that it looks like the one for the Flag module.

What I'm trying to say is that it seems that saving a new or existing template without selecting a bundle will PERMANENTLY transform it from being a template for the Flag Lists module into a template for the Flag module.

As for a potential solution, fixing what I said in a similar issue → (#8) will probably take care of this issue too. But I'm still reporting this as a separate issue because it might give you some new insights while you try to get the recent patch → (#7) fully working.