Simple clamper circuit - ambiguous math - What's the catch?
Your scenarios look to be both mathematically correct and, in practice they will both be correct (but at different periods of time). During some parts of the AC cycle the diode will loosely clamp the most negative portion of the input waveform to about -0.6 or 0.7 volts then, when the waveform is more positive the diode won't be clamping.
Hence, what you describe is not the full story about a clamper circuit. Try simulating it and see what happens.