I would understand it the same way.
Displaying the unedited badges (with a proper reference and attribution) - totally fine.
Using different requirements for the (same) badges - no.
Building a new badge system (other graphics and requirements) - I guess it depends on how big the differences are.
We know there are quite similar systems out there, but there are distinct enough and all build on the old BadgeGen, which was considered abandoned, and several people developed it individually.
Maybe you can reach out to us (also via GC Message or email) and explain a little what you have in mind? Maybe it could directly get integrated into BadgeGen. :)