Precision Rectifier confusion
You haven't provided details about how you are measuring the signals, but I'm going to guess that you are using an oscilloscope with 10 Meg probes.

The drawback of this circuit topology is that the output impedance is different between positive-going half-cycles and negative (on the input).  The output impedance is essentially zero for negative half-cycles but is the sum of the two resistors for positive half-cycles.

In your second example, the output impedance of the rectifier is 200k.  Work out what the voltage drop is with your 10M scope probe and you will most likely find the value that you calculate matches what you are measuring.