That example falls short. Not seeing a fly is not the same as not seeing an elephant. What size is the room? Is there something big enough to hide an elephant or fly? What methods were used to look?
There are some exceptions, to be sure, but in your examples it is 100% reasonable to find the evidence if one is willing to look. Also, we know what flies and elephants are, their properties, etc., and how to detect them. In the case of god, anytime someone has been able to loosely define what we are looking for, then absence of evidence absolutely is evidence of absence.
It is not my example and it is simple to help laymen understand the logical fallacy and it's exceptions. It can be dissected like this but it is used to convey a point and assist in understanding.