Input Voltage vs Output Voltage for a Shunt Positive Clipper with Bias Voltage
It would be helpful to put an explicit RL load resistor on that diagram. All that you say is correct, except for the fact that you're confusing the times when RL is absent, or large, or small.

The circuit always clips when Vout > V + 0.7 V.

If RL is absent or very very large, then Vout = Vin, so the same eqaution applies to Vin.

If RL is significant, you need to take account of its voltage divider action with R, before you write clipping conditions for Vin.