I want to explore two areas: Scope and terminology.
There are systems at (at least) two different scopes here: The end-to-end system and the unit, which is also a system.
When I'm analyzing a "defect," I like to think in terms of three parts: Failure, fault, and conditions. The failure is the system's production of incorrect results. The fault is the erroneous element of the system that, under certain conditions, leads to the failure. Though the fault is always there in the system, I may or may not observe a failure, depending on the conditions.
Given that, I would say you have not reproduced "the defect" in a unit test. That is, you have not reproduced the same failure. You have (perhaps) isolated the fault, and you have produced a different failure: a failure at the scope of the unit.
No unit test can verify end-to-end behavior. A unit test may give you confidence in the end-to-end behavior, but your confidence comes from inference, not observation. And your inference is based on your mental model of the system.
So the wisdom of relying only on the unit test rests on a few questions: How good is your mental model of the system? How valid is your reasoning, given your model?
If people are talking about "the same defect" at different scopes, that tells me they have a distorted model of the system. In particular, their model does not distinguish between a unit failure and an end-to-end system failure. I would be skeptical of any inferences people make based on a model that is distorted in that way.