I am not sure references are easily faked. Especially in industries where there aren't a whole lot of references that someone is not going to know. "Hey Bob, I have this excellent candidate for the position you are looking for they have X qualities", much more likely to get an interview than the person from Indeed. That's simply reality.

As for a manager, you may not have their contact information, but seems like relevant information to keep ahold of for professional networking. So yes, it seems like you are making easy excuses that in a competitive hiring environment would quickly get you excluded from the pool of applicants.