Inverted signal in biopotential circuit
Diodes follow the Shockley diode equation pretty well at low currents and voltages, so in that sense they work just fine below 0.7 V. \$V_f \approx 0.7 {\tt\ V}\$ is just a designer's rule of thumb for a forward-biased silicon diode conducting "significant" current. The actual characteristic is more like a smooth exponential function.

The precision rectifier circuit compensates for the exponential characteristic of the diode with feedback from the op-amp. This works, but it still has trouble with very small signals. You can swap the polarity of the diodes in the precision rectifier to get a different polarity output.