Just wanted to confirm something - The other group you are referring to cloned your program in order to put it in the nurture campaign they are working in correct? That is the only way you can have two of the same programs in different nurture programs. If that is the case then you removing the program from your stream shouldn't impact their reporting. You can have the same email names, report names, and list names, but because it is in a different program they are actually pulling different information.
EX - Program One's name is Breather Nurture and assets are email, thank you, and webinar. These would then be tied to the breather funnel as BreatherNurture.Email
Program Two uses the same assets but is called Retarget Nurture thus the assets are now tied to this funnel differently. RetargetNurture.Email
This link may help as well. Clone a Program - Marketo Docs - Product Docs
Also, If you have any other questions I would suggest you move this to the products tab or marketing central because the champions program is more about learning how to become a champion. Not an expert QA group.