IANAL but the impression I get is that loosely defined terms like "tamper" can be interpreted in many different contexts depending on how eager the prosecutor is.

Falsifying your identity to a federal postal service to gain access to someone else's mail? That breaks a wide range of laws

Right -- falsifying identity to get postal resources would be a relevant category of crime. I don't see how mere non-destructive observation of the external packaging would count as tampering though.