Tunneling spectroscopy cannot be used as an unambiguous detection tool for Majorana zero modes (MZMs) in conventional partial-shell nanowires. The presence of smooth confinement at the end of the hybrid wire (among other sources of disorder) can create exponentially pinned zero-energy states, called quasi-MZMs, that mimic all local signatures of MZMs but lack topological protection. We find that this ambiguity in MZM detection does not occur in full-shell hybrid nanowires, an alternative nanowire design where a superconducting shell fully surrounds the semiconductor core. Acting as a synthetic vortex, a full-shell hybrid nanowire hosts Caroli-de Gennes-Matricon state analogs. In the presence of smooth confinement, these states create a topologically trivial skin at the wire's end that prevents the local probe from detecting quasi-MZMs. In this way, the same mechanism that creates MZM impostors makes them invisible in tunneling spectroscopy, avoiding false positives produced by smooth disorder.